We use effective field theory to factorize production matrix elements that appear in quarkonium cross sections in NRQCD. By applying a Hubbard-Stratonovich transformation we show that the soft and ultrasoft sectors of NRQCD can be decoupled from the heavy quark and antiquark fields in a hybrid vNRQCD/pNRQCD Lagrangian at leading order in the velocity power counting. This enables us to separate quarkonium production matrix elements in terms of matrix elements of color-singlet composite fields, which we can write as the wavefunction at the origin, and state independent vacuum correlators of chromo-electric and chromo-magnetic gluon fields. This approach verifies powerful connections between the LDMEs of different S-wave vector quarkonium states, originally derived using pNRQCD. Additionally, we find new operator contributions for the color-octet P-wave mechanism, which satisfy a similar set of relationships. Finally, this approach allows us to factorize the production matrix elements that appear in the transverse momentum dependent factorization framework, known as TMD soft transition functions, in terms of state independent gluon correlators. This work restores some universality for TMD production operators and dramatically improves the predictive power of NRQCD in the TMD framework.

The evolution of galaxies is profoundly influenced by the environment in which they reside. Cosmic voids serve as pristine laboratories for studying galaxy evolution in the relative absence of the complex physical processes that dominate denser environments. In this study, we investigate galaxy properties and merger histories as a function of environment using the GAlaxy Evolution and Assembly (GAEA) mock-observation lightcone replicating the Euclid Deep Survey as foreseen for the first Euclid data release. The H$α$-selected galaxy sample spans the redshift range $0.4 < z < 1.8$, corresponding to the interval over which H$α$ is accessible to Euclid slitless spectroscopy. We classify galaxies based on their void-centric distance and local density contrast, and compare their stellar mass, specific star formation rate, bulge-to-total stellar mass ratio, and halo mass across different environments. We further analyse the merger histories of these galaxies to study their assembly evolution. We find that galaxies located closer to void centres ($d_{\rm cc} \lesssim 0.7 R_{\rm v}$) are less massive, more actively star-forming, and more disc-dominated than galaxies in denser regions. Merger histories indicate that void galaxies do not experience fewer mergers, but rather that mergers occur later relative to galaxies in high-density regions. These results support a scenario in which the environment regulates the timing and nature of mergers rather than their overall frequency, producing a slower evolutionary path in low-density regions. We conclude by discussing the extent to which these trends are shaped by environmental parametrisation methods and observational selection effects. Our analysis provides a framework for interpreting forthcoming Euclid data and demonstrates Euclid's potential to identify cosmic voids and probe environmental effects on galaxy evolution.

We prove that a very general complex symmetric Verra fourfold is not \(\ZZ/2\)-birational to \(\PP^4\), using the \emph{theory of atoms} introduced by Katzarkov--Kontsevich--Pantev--Yu~\citep{Katzarkov2025BirationalIF} in the equivariant setting as in Cavenaghi--Katzarkov--Kontsevich~\citep{cavenaghi2026atomsmeetsymbols}.

We investigate the structural and operator-theoretic foundations of indirect signal-generation mechanisms in Keller--Segel-type chemotaxis models. By analyzing a physically motivated multi-stage signaling cascade, we establish a precise mathematical dichotomy between instantaneous equilibration and transient kinetic memory. Specifically, we prove that the fully equilibrating parabolic--elliptic--elliptic (PES) cascade reduces to a static fourth-order elliptic interaction. In dimension four, an exact algebraic cancellation of the leading Newtonian singularity yields a purely logarithmic kernel, shifting the mass-critical dimension from $N=2$ to $N=4$. Through an $L^2$-gradient flow formulation, we identify the corresponding concentration-scaling candidate critical mass $M_* = 64π^2τ/χ$. In sharp contrast, we demonstrate that the mixed elliptic--parabolic (MEP) cascade retains a genuine Volterra memory effect that defies static reduction. Its interaction drift acts as a singular perturbation in time-exhibiting classical two-dimensional Keller--Segel principal order near the time diagonal, yet providing fourth-order smoothing in its frozen-time average, necessitating a mixed space-time threshold theory. These results isolate the physical origin of mass-critical dimensional shifts in multiscale biological systems and formulate the specific adapted Adams/logarithmic Hardy--Littlewood--Sobolev (log-HLS) inequalities and mixed-norm criteria required to close the threshold problems.

JWST has enabled new high redshift observations with 14 spectroscopically confirmed galaxies at $z > 10$ to date, leading to a need for high redshift, high resolution simulations to interpret these observations. We present the physical properties and mock observations of the galaxies in the Renaissance Simulations to add to the growing database of high redshift simulation data to guide and interpret observations. We find that they provide an accurate representation of the formation history of JWST's $z > 10$ discoveries and follow the trends observed in JWST galaxies but extended to lower masses. The stellar masses of the Renaissance galaxies range from $\approx 10^{3}$ to $10^8 M_{\odot}$ and overlap well with the $z > 10$ JWST galaxies with a stellar mass range of about $10^{7}$ to $10^9 M_{\odot}$. The simulated SFRs increase from $10^{-4}$ to $10^1 M_{\odot}yr^{-1}$, overlapping the JWST galaxies' lower SFRs in the range $1 - 20 M_{\odot}yr^{-1}$. These compact galaxies show minimal morphology change as their stellar masses increase with the majority of the half light radii between $1$ and $10$ pc and the majority of the half stellar mass radii around $0.1$ kpc; their Sersic indices vary between $0$ and $4$. The Renaissance galaxies are bluer and generally transition well into the absolute UV magnitudes of the JWST galaxies in the main sequence of galaxies. Overall, our simulations agree well with JWST's discoveries to date, making them a valuable tool in the continued effort to understand the high redshift Universe.

Galaxy cluster strong gravitational lensing plays a central role in precision cosmology, yet robust theoretical predictions have lagged behind an abundance of high-quality strong lensing observations. This shortfall reflects both a mismatch between the geometry of the strong-lensing problem and standard cubic simulation boxes, and the fundamental tension between simulation volume and resolution. Consequently, many current forecasts adopt hybrid approaches that extract individual lenses from simulations and combine them with analytic or observed source populations positioned near caustics. These methods often omit correlated and/or uncorrelated line-of-sight (LoS) structure, or include it in ways that do not preserve correlations across redshift. Here we present a fully simulation-based procedure that generates strong-lensing images directly from particle data, drawing the lens, source, and all intervening resolved objects self-consistently from the simulated large-scale structure. Our approach combines a structure-preserving remapping of the simulation volume into a lensing-appropriate geometry with multi-plane ray tracing, enabling the use of uniform simulation boxes that resolve both cluster-scale primary lenses and high-redshift source galaxies. We demonstrate the method by generating example light cones and images using IllustrisTNG data, then use these results to conservatively quantify the impact of LoS structure on image configurations and critical-curve morphology. We find that uncorrelated LoS structure can shift the relative positions of lensed images by several arcseconds, introduces a $\sim 6\%$ scatter in the area of a cluster's primary critical curve, and changes the total critical area within 100$^{\prime\prime}$ of the cluster potential minimum by $16^{+20\%}_{-14\%}$ at a source plane redshift of $z_s=4$.

A long-standing problem in the simulation of neutron star spacetimes is the treatment of vacuum regions outside the stars. The use of an artificial low-density atmosphere is a common robust approach within Eulerian hydrodynamics that, however, introduces baryon-mass violation even with conservative numerical schemes. We propose a simple numerical algorithm that ensures exact mass conservation by means of an appropriate local rescaling of the atmosphere. The scheme is combined with a low-order flux correction and it can be further augmented by a pseudo-vacuum treatment that enforces strict vacuum in the outer regions far from the central objects. We demonstrate the effectiveness of these vacuum treatments with binary neutron star mergers simulations spanning multiple orbits and the postmerger phase, and including a microphysical equation of state. The rescaling algorithm guarantees mass and electron number conservation to round-off precision. The pseudo-vacuum treatment shows slightly larger but approximately constant violations and can improve the computation of fast tail ejecta as well as provide convergent gravitational waves of quality comparable to the standard atmosphere. Overall, results from different atmosphere treatments and a two-code comparison suggest that current computations of gravitational waves and (dynamical) ejecta in the presence of an artifical atmosphere are robust, provided that conservative adaptive mesh refinement with flux correction is employed.

In the recent article [arXiv:2605.18966], we demonstrated that finding Clifford symmetries can be mapped to a Graph Automorphism (GA) problem. Here, we provide an algorithm to obtain such symmetries on general qudit systems, that works on the principle of encoding Clifford invariants of a Hamiltonian onto properties of a graph. Labelling Hamiltonian terms as vertices, a permutation of such vertices that respects the Clifford invariants (a GA) is both a valid Clifford, and a symmetry up to phase correction checks. We test this on multiple physical models and discuss the scaling with respect to the number of qudits and Pauli strings, as well as various strategies for optimisation in different regimes. We further show that the graph automorphism representation of Clifford symmetries can be expanded to open quantum systems.

We discuss the implications of the nebular dust attenuation curves derived for 24 galaxies at z=1.5-4.4 with multiple detections of HI Balmer and Paschen recombination emission lines from the JWST/AURORA survey. The total attenuation of Ha is ~0.20 dex larger on average than the values obtained with the commonly adopted combination of the Balmer decrement and the Galactic extinction curve. Nebular-line SFRs and SED-based SFRs are consistent on average when using the MOSDEF attenuation or SMC extinction curves for the latter. The relation between nebular and stellar reddening is consistent with a scenario where the Paschen lines are sensitive to heavily reddened OB associations, while relatively unreddened OB associations contribute significantly to the Balmer line and UV continuum emission. There is a stark contrast between the low Rv (or steepness) of stellar dust attenuation curves and the high Rv (or flatness) of nebular dust attenuation curves. We suggest that the latter could be reflective of a more porous medium established by strong feedback from massive stars. For the youngest galaxy in the sample, the stellar reddening curve is identical to the nebular attenuation curve, in accordance with our expectation that OB associations dominate the stellar continuum emission at all wavelengths for this very young galaxy. Larger samples will be needed to determine whether this conclusion holds for young galaxies in general, and provide further insights into the dust and metals mixing timescale on the scale of HII regions.

Positive non-Completely Positive (PnCP) maps are an essential tool to detect entanglement since their characterization is a dual aspect of the separability problem. A recent algorithm proposed by Kelp et al. explains how to generate PnCP maps based on the construction of certain positive non-Sum-of-Squares polynomials. We implement this algorithm in a numerically robust way and propose a working version on GitHub. We theoretically demonstrate that the maps produced by the algorithm are indecomposable, localized on the boundary of the positive cone and show that they are inequivalent with most other known PnCP maps. We numerically investigate their entanglement power, demonstrating notably that they are capable of detecting PPT entangled states that most criteria fail to detect.

Superconducting microwave circuits with and without Josephson inductances are the Swiss Army knife for many experiments and technologies from quantum information science to astrophysical particle detectors. Despite a large variety of existing circuit types, thin film materials and Josephson junction technologies, a flexible and reliable platform for high-magnetic-field and high-temperature applications is yet to be found. In this manuscript, we investigate coplanar waveguide cavities made of the high-temperature cuprate superconductor YBa$_2$Cu$_3$O$_7$ (YBCO), integrated with Josephson inductances and quantum interferometers that are generated by the controlled local irradiation of the YBCO with a focused helium ion beam. We obtain strongly flux-tunable microwave resonators, which not only display periodic interferometer oscillations of resonance frequency and decay rate, but also a superimposed Fraunhofer-like modulation pattern. The latter originates from the magnetic field tuning of the individual Josephson junction critical currents due to the out-of-plane junction barriers. It allows adjusting resonance frequency and flux responsivity independently of each other, potentially enabling tunable microwave circuits with low sensitivity to external magnetic-field noise over a broad range of frequencies. Finally, we investigate the temperature dependence of the cavities, show that they have promising characteristics up to 14$\,$K, and present a model for the junction-induced cavity losses.

We report the detection of the high-ionization line [NeV]$λ$3427 in the JWST/NIRSpec archival spectra of 6 massive quenched galaxies at $z \sim 1.5-4.5$, identified from a parent sample of 87 systems. With an ionization potential of approximately 97 eV, [NeV] can only be produced by strong nuclear activity in these massive systems, providing a clean and unambiguous tracer of highly accreting supermassive black holes uncontaminated by residual star formation. For 4 of the 6 [NeV]-detected systems, we detect broad H$α$ emission ($\mathrm{FWHM} \gtrsim 4000$ km s$^{-1}$), yielding black hole masses of $M_{\rm BH} = 10^{8.5-9.5}\,M_\odot$, consistent with local scaling relations with stellar mass and velocity dispersion. The [NeV] luminosities imply quasar-like bolometric outputs ($L_{\rm bol} = 10^{45-46}$ erg s$^{-1}$) and Eddington ratios of $λ_{\rm Edd} \approx 10$-$50$%, with black hole accretion rates of a few $M_\odot$ yr$^{-1}$ that match or exceed the residual star formation rates in the most extreme cases. The strongest [NeV] emitters are preferentially found in the youngest post-starburst systems ($D_n4000 \lesssim 1.3$), while old quenched galaxies are systematically devoid of such activity, a trend independently reproduced by theoretical models. These results reveal that intense, radiatively efficient SMBH growth can persist several hundred Myr after the main quenching epoch, with duty cycles of approximately 100-200 Myr. They also underscore the importance of very high accretion episodes and rates in the theoretical models that seek to reproduce the earliest quenched galaxies in the universe.

The Euclidean de Sitter path integral contains the familiar phase associated with conformal negative modes. Maldacena's construction shows that a suitably included real observer can reorganize the refined state-counting problem. This paper does not rederive that cancellation. It addresses the prior semiclassical admissibility question: which observer sectors couple to the de Sitter saddle as genuine metric observers without becoming spectators or producing infrared-singular backreaction? On $S^D$, after gauge fixing and zero-mode projection, the observer's quadratic influence is governed by a Schur complement. We formulate a form-domain criterion: if the observer kernel is positive and the mixed metric-observer source is bounded after applying $Δ_{ΦΦ}^{-1/2}$, the induced metric correction is a bounded quadratic-form perturbation on the chosen channel. In the gapped case, $Δ_{ΦΦ}\geq m_*^2\mathbf{1}$ gives $\|K^\dagger Δ_{ΦΦ}^{-1} K\|_{\rm op} \leq \|K\|_{\rm op}^2/m_*^2$; metric-coupled soft modes produce corrections growing as $1/\varepsilon$. We prove a sufficiency theorem: on any stable channel with coercive form $Q_{gg}^P \geq δ_P \|h\|^2$, the Gaussian saddle remains controlled whenever $\|Δ_{ΦΦ}^{-1/2} \mathfrak{j}_P\|_{\rm op}^2 < δ_P$. We construct a localized gapped clock-detector with internal oscillators on a smeared worldline that satisfies the criterion with a computable bound and gives explicit $S^4$ benchmark versus the round-sphere TT scale. The conformal channel is treated only as an indefinite or contour-defined sector; boundedness does not imply positivity. The criterion identifies the semiclassically admissible observer class. Phase cancellation follows only when this class overlaps the relevant conformal or negative-mode sector and is combined with an independent contour or state-counting prescription.

We investigate the effect of millicharged particles (MCPs) with electric charge $qe\ll e$ and mass $m_χ$ on the late-stage evolution phases of low-mass stars in globular clusters. We predict the $R_2$ parameter -- the ratio of the number of stars in the asymptotic giant branch (AGB) phase to the number of stars in the horizontal branch (HB) phase -- and compare it against globular cluster data. While the production of MCPs shortens both the HB and AGB lifetimes, a larger reduction in the AGB phase arises from the higher temperatures in the helium-burning shell. We find the strongest bounds in the range $10\,\mathrm{keV}\lesssim m_χ\lesssim 100\,\mathrm{keV}$, reaching charges as small as $q\simeq 5\times10^{-13}$ and surpassing existing constraints by up to two orders of magnitude.

We present a new class of topological phenomena in inhomogeneous systems arising from the adiabatic spatial embedding of parametrized families of quantum states such as charge pumps and their generalizations. We demonstrate that each topologically distinct class of these "diabolical textures" gives rise to distinct gapped states that are separated by "trap-scaling" critical points. When the texture varies sufficiently rapidly in space, the critical line terminates abruptly, producing an "unnecessary critical" surface. We demonstrate our results using a microscopic model of non-interacting fermions with a spatially embedded Thouless pump. We study its phase diagram comprehensively and establish its stability to arbitrary perturbations, including interactions, in the vicinity of the critical regions. For systems in arbitrary spatial dimensions and global symmetries, we present a framework to systematically classify diabolical textures using Kitaev's $Ω$ spectrum conjecture.

The detection of near-Earth asteroids (NEAs) is critical for planetary defense and for advancing our understanding of the small-body population in the Solar System. Traditional detection techniques, including optical and radar, are the cornerstone of NEA discoveries. However, these are limited by observational constraints. We investigate whether the Laser Interferometer Space Antenna (LISA), a future space-borne gravitational wave detector, might detect and constrain the parameters of NEAs through their gravitational effect on the spacecraft test masses during a close approach at the minimum orbital intersection distance. We modeled the gravitational perturbations of the test masses on the LISA spacecraft exerted by a passing NEA. Based on this, we computed its signal-to-noise ratio (S/N) to determine detectability using the LISA requirements. Furthermore, we used the Fisher information formalism to estimate the uncertainties on the state vector and mass of the asteroid given it is detected. These estimates provide a first-order assessment of the LISA capability to resolve NEA parameters under favorable encounter geometries. The Fisher information study showed that the fractional uncertainty on the asteroid mass scales as the inverse of the S/N. Consequently, a detection with an S/N $\geq 5$ yields a mass determination with an uncertainty of $\sim20\%$ at most. In contrast, the state vectors exhibit considerably larger uncertainties as they depend significantly on the geometry of the close approach. Nevertheless, for very high S/N cases, this precision may be comparable to the uncertainties obtained by some of the current observational methods. The analysis of the correlation matrices confirms that each close encounter produces a specific signal and provides a practical means to assign independent error bars to the recovered state vector.

In this work, we broach a quantum information-theoretic treatment of axion--photon mixing. Motivated by an emerging class of quantum-enhanced axion searches, we analyse the two-level single-excitation sector of axion--photon oscillations, demonstrating how the coupled dynamics naturally generate bipartite axion--photon mode entanglement. We study in detail the ensuing aspects of entanglement entropy, concurrence, negativity, quantum mutual information and discord, and capacity of entanglement, and the corresponding neutrino analogues wherever novel and previously unaddressed. In particular, we highlight the characteristic features that connect maximal axion--photon entanglement to resonant or strong-mixing conversion, and the distinct thresholds for the extremal values attained by the quantum information measures. We study aspects of the Mandelstam--Tamm and Margolus--Levitin quantum speed limits for both the axion--photon and neutrino systems. While orthogonalisation occurs only at axion--photon resonance, or at maximal neutrino mixing, where the two bounds coincide, away from these limits, the Margolus--Levitin bound is saturated at maximal conversion, while the Mandelstam--Tamm bound is generally weaker. We also study an entanglement quantum speed limit for axion--photon conversion, that separates into detuning-dominated and magnetic-mixing-dominated regimes, and find that it is saturated for a period and then the bound becomes weak. The results in this work identify the quantum resources and limiting timescales intrinsic to axion--photon conversion, and connect axion phenomenology, neutrino oscillations and quantum information theory.

We propose a sigma-model analogue of Hodge loci in the moduli space of geometric Calabi-Yau compactifications, characterized by the emergence of non-trivial rational Hodge endomorphisms, using generalized symmetries. In the CFT description, the complex cohomology is spanned by Ramond-Ramond ground states, the Hodge decomposition is determined by the $U(1)\times U(1)$ R-charges, and the rational structure is provided by BPS boundary states, with polarization induced by the open string Witten index. Hodge loci are identified by the existence of a non-trivial category $TDL$ of topological defects preserving the $N=(2,2)$ superconformal algebra and acting invertibly on the spectral-flow generators. At special points on these loci, the category $TDL$ exhibits additional arithmetic structure and admits embeddings of finite products of number fields with Complex Multiplication, leading to stronger constraints on the boundary states of the theory. Although the construction is general, we analyze in detail the cases of elliptic curves and $K3$ surfaces.

Logarithmic correction to BPS black hole entropy, computed from microscopic description, often contains terms involving large ratios of charges, besides the logarithmic terms involving the overall scale of the charges. If the electric charges are much larger than the magnetic charges, then the attractor value of the string coupling is small and one might hope to use weakly coupled string theory to compute logarithmic corrections involving ratios of charges from the macroscopic side. We compute these for black holes in flat space-time, preserving four supercharges, in $\mathcal{N} = 2$, $\mathcal{N}=4$ and $\mathcal{N}=8$ supersymmetric string compactifications in four dimensions. We find perfect agreement with the microscopic results in $\mathcal{N}=4$ and $\mathcal{N}=8$ theories, for which the microscopic results are known. Various stringy and statistical mechanical effects become important in this analysis, including 1) use of the correct ultra-violet cut-off (string scale instead of Planck scale), 2) correct path integral measure (ultra-local measure with appropriate dilaton dependent metric), 3) use of the correct path integral variable (Kalb-Ramond 2-form instead of the dual axion) and 4) change of ensemble (from grand canonical to microcanonical). We also verify that the measure we use is consistent with what follows from the BV formalism of string field theory.

Axion-like particles coupled to photons are one of the most compelling new physics scenarios. We demonstrate that an axion-photon coupling resulting from a non-anomalous PQ symmetry under which light fermions are charged acts as a bandpass filter: both high- and low-energy probes experience a parametrically suppressed coupling while intermediate-energy probes remain unaffected. An immediate result of this bandpass is that lab-based constraints can naturally be the dominant constraint for almost all values of the axion mass. High-energy constraints coming from stellar dynamics as well as low-energy constraints coming from photon-axion conversion in galactic/stellar magnetic fields are simultaneously suppressed, while lab-based experiments, such as light-shining-through-a-wall experiments, done at intermediate energies are unsuppressed.

Spectroscopic observations from JWST have uncovered a plethora of active galactic nuclei (AGN) at z > 4 with black hole (BH) mass (Mbh) to stellar mass (M*) ratios significantly above the local relation when using standard virial mass scaling relations. However, M* estimates of AGN may be inaccurate due to limitations in spectral energy distribution (SED) fitting codes, exemplified by a lack of physically-motivated AGN line emission models. Here, we fit NIRSpec/PRISM spectra of 39 galaxies at z ~ 3.5-7 selected as broad-line AGN from the CEERS and RUBIES surveys. Applying kinematic decompositions from NIRSpec/G395M spectra, we fit their continuum and narrow-component line fluxes using the BEAGLE-AGN SED fitting tool. While limitations of BEAGLE-AGN make it difficult to model little red dots (LRDs), we find that M* estimates of non-LRDs are, surprisingly, only modestly impacted by the inclusion or not of AGN narrow-line region (NLR) and continuum emission model components. We further find that non-LRD AGN at z < 3.5 are consistent with the local Mbh/M* relation while those at z > 4.5 display elevated ratios. While we cannot rule out observational biases or systematic uncertainties as partial causes, this transition over just ~500 Myr is driven entirely by changes in M* rather than an evolving Mbh distribution. These findings are consistent with models in which rapid BH growth results in elevated Mbh/M* ratios at early times, with a swift late-time assembly of host galaxies returning sources to the local relation at z < 4.

We present an $SU(12) \times SU(2)_L \times U(1)_R$ model unifying $SU(9)$ quark color-flavor with $SU(3)$ lepton flavor as a flavorful alternative to conventional theories of unification. We begin in the ultraviolet with a single yukawa shared by the unified up-type quarks and neutrinos, and no further new fermions. We show that gauged quark color-flavor and lepton flavor instantons dynamically generate the bottom and tau yukawas, which implements a massless quark solution to the strong CP problem and sets up a flavored type-I seesaw mechanism. Only two new scalar irreps are needed for the symmetry-breaking steps, which include quark color-flavor deconstruction and then infrared reunification, and the Standard Model gauge group in this theory emerges as \[G_{\rm SM} = \frac{SU(3)_C \times SU(2)_L \times U(1)_Y \times \mathbb{Z}^X_{18}}{\mathbb{Z}_{3} \times Γ\times \mathbb{Z}_3},\] where $Γ\in \lbrace 1, \mathbb{Z}_2 \rbrace$ is the electroweak global structure and there is a discrete gauge symmetry $X = B - 3(L_i + L_j - L_k)$ which brings additional $\mathbb{Z}_3$ global structure to the SM. This gauge symmetry acts as a flavorful upgrade of the $\mathbb{Z}^{B+L}_{18}$ anomaly-free global symmetry of the SM and stabilizes the proton absolutely. Non-invertible chiral symmetry-breaking is crucial to our model, and we discuss the rich spectrum of emergent generalized symmetries and topological defects appearing at various stages. In the infrared, the novel shared quotient between continuous and discrete groups links the one-form and two-form global symmetries of the Standard Model.

We show that axions cause extremal black holes to have singular horizons. This is true for almost all values of the axion mass and coupling provided the black hole is rotating and has some arbitrarily small nonzero charge. When the axion mass becomes large, these singularities are related to the recently discovered singularities induced by higher-derivative corrections to the Einstein-Maxwell equations. Away from extremality, this effect produces anomalously large tidal forces in the vicinity of near-extremal horizons, causing breakdown of the effective theory.

High-redshift galaxies have smaller radii, harder ionizing continua, and higher ionizing photon production efficiencies than lower redshift systems, which implies a corresponding evolution in nebular conditions. A key metric to quantify gas properties is the ionization parameter, q, the ratio of the local ionizing photon flux to the local hydrogen density. The ionization parameter is often inferred from observed emission line ratios, e.g., O32=[O III]/[O II]. Prior to JWST, statistical samples of ionization parameter-sensitive emission lines in the rest-frame optical remained inaccessible at high-z. We investigate the dimensionless ionization parameter, U=q/c at 3<z<9, inferred using Cloudy photoionization models from the O32 ratios for 434 galaxies in the RUBIES survey with JWST/NIRSpec PRISM and G395M spectroscopy, constituting the largest high-z population study of U to date. We compare to lower-redshift samples from SDSS, LEGA-C, and KBSS to probe the evolution of U from 0<z<9. We find that U increases with redshift and specific star formation rate (sSFR), and decreases with stellar mass. We combine the predictive power with multivariate relations to estimate U from redshift, stellar mass, and sSFR for use in cases where O32 is not available from spectroscopy, and show that U increases with redshift even at fixed stellar mass and sSFR by a factor of ~4 from z=2 to z=6. Crucially, and in contrast to previous linear best-fit calibrations, our inference results in a systematic uncertainty in log U of ~0.3 dex at zero measurement uncertainty due to the wide range of photoionization models that predict the same O32 ratio without informative priors. Finally, we discuss future modeling frameworks to accept many observed emission lines to simultaneously constrain gas-phase abundances, densities, ionizing sources, and ionization parameters to high accuracies for individual galaxies.

Killing forms on finite groups arise as special cases of braided Killing forms on braided Lie algebras. If $\mathcal{C}$ is a conjugation-stable subset of a finite group $G$, the Killing form on $\mathbb{C}\mathcal{C}$ is given by $K_\mathcal{C}(a,b) = |C_G(ab) \cap \mathcal{C}|$ for $a,b \in \mathcal{C}$. It is conjectured in previous work by López Peña, Majid and Rietsch that $K_\mathcal{C}$ is non-degenerate for any real conjugacy class $\mathcal{C}$ in a finite simple group. In this article, we reformulate the conjecture and introduce combinatorial conditions - the $\textit{1-element condition}$ and the $\textit{2-element condition}$ - that are sufficient for non-degeneracy to hold. This allows us to prove the conjecture for simple groups of the form $\mathrm{PSL}_2(q)$ and certain conjugacy classes in the alternating and symmetric groups. Moreover, we verify computationally that every real conjugacy class in a simple group of order $\leq 10^9$ fulfills at least one of these two conditions, thereby significantly extending the computational evidence for the conjecture. This raises the question whether these conditions are satisfied by all conjugacy classes in finite simple groups.

We put forward a quantum model of cosmology that is exactly periodic but avoids the Boltzmann Brain problem. If the universe is described by a quantum state evolving unitarily in a finite-dimensional Hilbert space, its evolution will be recurrent: given enough time, the state will return arbitrarily close to its initial state. There is a worry that such a scenario cannot be phenomenologically acceptable, because the state will spend most of its time in a high-entropy equilibrium macrostate, with rare fluctuations downward in entropy, and the vast majority of observers will be minimal fluctuations away from equilibrium, or ``Boltzmann Brains." Here we show that this is not necessarily true. If the differences in energy eigenvalues are commensurable, the evolution is not simple recurrent, but exactly periodic. Moreover, if the state starts at minimum thermodynamic entropy, its evolution can feature a distinguished entropy excursion that is much more pronounced than one would expect from the conventional expression $P(ΔS) \propto \exp(-ΔS)$. This excursion could represent our Big Bang, with relatively few Boltzmann fluctuations occurring in the subsequent equilibrium phase before a Big Crunch occurs and the cycle begins again. We speculate on the spacetime interpretation of this kind of quantum universe.

The precise determination of the leptonic CP phase $δ_{\rm CP}$ remains one of the central objectives of current and future long-baseline (LBL) neutrino oscillation experiments. Quantum estimation theory provides a natural framework to quantify the ultimate precision limits for estimating physical parameters encoded in quantum states. In this work, we employ the quantum Fisher information to investigate how much information about $δ_{\rm CP}$ is intrinsically encoded in neutrino states and how efficiently it is extracted in present LBL experiments such as T2K and NO$ν$A. We first analyze the intrinsic quantum sensitivity of neutrino and antineutrino states and demonstrate how matter effects generate a neutrino mass-ordering dependent information structure. To compare the intrinsic information content of the quantum state with the information experimentally accessible through flavor measurements, we compute the event-level Fisher information from reconstructed event spectra using Poisson statistics. We find that both experiments extract only a small fraction of the total information available in the underlying quantum state. This extraction efficiency becomes particularly suppressed near maximally CP-violating regions, where the reconstructed event spectra exhibit reduced sensitivity to small variations in $δ_{\rm CP}$. Our analysis provides a complementary information-theoretic perspective on precise estimation of oscillation parameters in LBL neutrino experiments.

We investigate a planar Dirac oscillator coupled to a spatially uniform \(\utwo=\uone\times\su\) Yang--Mills background. The gauge configuration, adapted from the Dossa--Avossevou construction, contains an Abelian magnetic field \(B\), a non-Abelian spatial amplitude \(β\), and a non-Abelian scalar amplitude \(ρ\). Within the Pauli-reduced formulation, the non-Abelian field strength produces a constant operator on \(\mathbb{C}^{2}_{\mathrm{spin}}\otimes\mathbb{C}^{2}_{\mathrm{iso}}\). This operator contains a diagonal internal-Zeeman contribution proportional to \(σ^{3}T^{3}\) and an off-diagonal spin--isospin term proportional to \(σ^{1}T^{1}+σ^{2}T^{2}\). Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues \[ λ_{\mathrm{FM}}=\frac{g^{2}β^{2}}{4m},\qquad λ_{S}=-\frac{g^{2}β(β-2ρ)}{4m},\qquad λ_{T}=-\frac{g^{2}β(β+2ρ)}{4m}. \] Consequently, the aligned internal-Zeeman scale is quadratic in \(β\), whereas the singlet--triplet separation is linear in \(βρ\). The revised formulation makes the sign conventions explicit, verifies the main limiting cases, distinguishes the Pauli-reduced spectrum from a full first-order Dirac diagonalization, and clarifies the physical meaning of the numerical illustrations.

For a simple graph $Γ$ and a real number $λ$, the general reduced second Zagreb index is defined by the formula $$GRM_λ(Γ)=\sum_{ab\in E(Γ)}[(°_Γ(a)+λ)(°_Γ(b)+λ)]\,.$$ A sharp lower bound for $GRM_λ$ over all trees of given order and maximum degree under the condition that $λ\ge -\frac{1}{2}$ is established. A parallel result is proved for unicyclic graphs under the condition $λ\ge -\frac{1}{2}$. The corresponding minimal trees and unicyclic graphs are identified. These findings improve upon the lower bounds previously established by Buyantogtokh, Horoldagva, and Das concerning $GRM_λ$ of trees and unicyclic graphs of given order.

We give a small sparse-generic counterexample to a rank-intersection conjecture of Brualdi, Friedland, and Pothen concerning elementary vectors in the row space of a matrix.