arXiv digest

15 September 2026

arXiv announcement of Tuesday 15 September 2026 (submissions received Fri 14:00 ET → Mon 14:00 ET) · 15 categories · source: rss.arxiv.org

1103 announcement entries read across 15 feeds · 494 unique new and cross-listed papers scanned · 51 passed the keyword pre-filter to Level 2 · 13 in the digest (score ≥ 3) + 2 bonus

Relevant papers

Neutrino mass and 0νββ6

Sebastian J. Figueroa, Alexander C. Sobotka, Adrienne L. Erickcek

The standard escape route from the cosmological mass bound — dilute the relic neutrinos by injecting photons after decoupling — does not work. Planck+ACT lensing+DESI give $\sum m_\nu<0.0710$ eV even when dark radiation comes along, and $T_\nu$ turns out to correlate positively with $\sum m_\nu$, so lowering the pre-recombination radiation density sharpens rather than relieves the tension with the measured splittings.

astro-ph.COhep-ph
Abstract

We investigate how neutrino-mass constraints from cosmology depend on the assumed thermal history of the universe. Photon injection after neutrino decoupling would decrease the neutrino abundance inferred from the temperature of the cosmic microwave background (CMB), potentially loosening the upper limit on their masses. We first evaluate how the cosmological neutrino-mass bound is altered by the decay of massive particles into photons and dark radiation after Big Bang nucleosynthesis. To test the robustness of this constraint more generally, we also assess the impact of varying the temperature of the cosmic neutrino background without assuming a specific physical mechanism. We perform MCMC analyses of both frameworks with primary CMB observations from Planck, CMB lensing measurements from Planck and ACT, and baryon acoustic oscillation data from DESI. For the degenerate mass ordering, the $95\%$ credible limit tightens from $\sum m_\nu<0.0691$ eV in a standard thermal history to $\sum m_\nu<0.0652$ eV if the massive particles decay only into photons, while the injection of dark radiation in addition to photons slightly relaxes this limit to $\sum m_\nu<0.0710$ eV. The same pattern holds for the normal and inverted orderings, and the decay scenario shifts the bound on the sum of the neutrino masses by at most $0.004$ eV for fixed mass splittings. Allowing model-agnostic changes in the neutrino-to-photon ratio yields a $95\%$ credible limit of $\sum m_\nu<0.0724$ eV for the degenerate ordering, indicating that the stringency of our neutrino-mass bounds is not driven by constraints on the decay scenario. We find that the neutrino temperature and the sum of the neutrino masses are positively correlated, which implies that reducing the pre-recombination radiation density will only worsen the emerging tension between cosmological bounds on the neutrino masses and the measured mass splittings.

Gabriela Barenboim, Marco Drewes, Isabel M. Oldengott

Starts from the neutrino quantum kinetic equations and derives the Boltzmann hierarchies in the mass basis, so mixing is carried through consistently instead of being assumed away. The payoff is a clean rescaling of existing CMB limits on the effective self-coupling: weaker by $\sqrt{2}$ when two flavours interact, by $\sqrt{6}$ when only one does, with $\nu_e$-only the one case where the fluid approximation degrades.

astro-ph.COhep-ph
Abstract

We study the impact of flavour-specific neutrino self-interactions on the CMB anisotropy spectrum and consistently take into account neutrino mixing. Starting from the neutrino quantum kinetic equations, we derive the neutrino Boltzmann hierarchies for the neutrino mass states. Our work shows that most scenarios of flavour-specific neutrino self-interactions are well approximated by a combined fluid approach. In practice, this implies that existing CMB bounds on the effective neutrino coupling are weakened by a factor $\sqrt{2}$ for scenarios in which only two neutrino flavours interact (irrespective of which flavours). If only one neutrino flavour interacts the bounds are weaker by a factor $\sqrt{6}$, with the only caveat that the combined fluid approach is less reliable for only $\nu_e$ interacting.

Yongchao Zhang, Zhong Zhang

Muon decay as a laboratory probe of neutrino self-interactions. The phenomenologically live channels — the one-loop correction to SM muon decay and the four-body $\mu^-\to e^-\nu\nu\phi$ modes — are both driven by the coupling $h_{e\mu}$ to Majorana neutrinos, and their infrared divergences cancel against each other. $G_F$ precision alone then gives $|h_{e\mu}|\lesssim0.027$, beating astrophysical and cosmological bounds for $m_\phi\gtrsim\mathcal{O}(\mathrm{GeV})$.

hep-phhep-ex
Abstract

The non-standard self-interactions of neutrinos could be induced by (light) scalars that couple primarily to neutrinos. In this work, we investigate the effects of neutrinophilic scalars $\phi$ on muon decays at the tree, 1-loop and 2-loop levels, considering both Dirac and Majorana neutrinos. The most phenomenologically interesting processes are the 1-loop corrections of $\phi$ to the SM muon decay and the four-body muon decays $\mu^- \to e^- \nu_\mu \nu_\mu \phi,\, e^- \bar\nu_e \bar\nu_e \phi$, both induced by the coupling $h_{e\mu}$ of $\phi$ to Majorana neutrinos. The infrared divergences in these processes cancel with each other, yielding an infrared-safe inclusive decay width. The precise $G_F$ measurements constrain the coupling $|h_{e\mu}|$ down to roughly $0.027$, with the scalar mass $m_\phi$ constrained up to roughly $5.9$ TeV. For $m_\phi \gtrsim {\cal O}({\rm GeV})$, the $G_F$ measurements are more stringent than other existing laboratory, astrophysical and cosmological constraints. Some other $\phi$-induced processes are also possible, which are, however, heavily suppressed by the small couplings, tiny neutrino masses and/or the loop factor.

Pankaj Borah, Satyabrata Mahapatra, Newton Nath et al.

A $\mathcal{Z}_2\times\mathcal{Z}_4$ structure that forbids the tree-level Dirac Yukawa and every renormalizable Majorana mass term, leaving neutrino mass Dirac and generated at one loop by a softly broken trilinear $\kappa$. The same $\kappa$ sets the singlet-doublet mixing, so the LZ inelastic rate and $m_\nu$ vanish together; the $Z$ coupling is purely off-diagonal by construction rather than by tuning.

hep-phastro-ph.COhep-exhep-th
Abstract

The LUX-ZEPLIN (LZ) experiment has reported a high-energy nuclear recoil candidate, LZ230616, at $E_R = 248 \pm 23_{\rm stat} \pm 23_{\rm sys}\,$keV, which is difficult to reconcile with elastic scattering of halo dark matter (DM). Endothermic inelastic scattering offers a natural explanation, but it rests on a nucleon coupling that is off-diagonal rather than diagonal. We show that this feature arises automatically within a radiative Dirac neutrino mass framework. The Standard Model is extended by three right-handed neutrinos (RHNs), a pair of vector-like neutral fermions for each generations, and a scalar sector comprising an inert doublet and a real singlet, governed by a $\mathcal{Z}_2 \times \mathcal{Z}_4$ symmetry. The $\mathcal{Z}_2$ symmetry stabilizes the DM, while the $\mathcal{Z}_4$ symmetry forbids the tree-level Dirac Yukawa coupling together with all renormalizable Majorana mass terms, thereby allowing the generation of Dirac neutrino masses at the one-loop level through a softly broken scalar trilinear coupling `$\kappa$'. Since the neutral dark-sector fields can be expressed in terms of real scalar mass eigenstates, the $Z$ boson couples to them purely off-diagonally and elastic $Z$-mediated scattering is absent identically rather than simply suppressed. The singlet--doublet mixing induced by `$\kappa$' governs both the inelastic rate and the one-loop Dirac neutrino mass, which therefore vanish as $\kappa \to 0$. We find that DM masses in the few hundred GeV to TeV range, with splittings of $\mathcal{O}(340-360)\,$ keV, simultaneously reproduce the observed relic abundance, account for the LZ event and yield neutrino masses of the correct order, while respecting elastic direct-detection limits and all relevant theoretical and experimental constraints. A substantial part of the surviving parameter space lies within reach of DARWIN.

Yu-Bing Li, Zhen-Dong An, Wei Jiang et al.

Neutron capture on $^{75}$As from 1 eV to 1 MeV measured by time-of-flight at CSNS Back-n: nineteen resonance structures seen for the first time and disagreements between evaluated libraries resolved. This is experimental input to the background and half-life modelling that $^{76}$Ge $0\nu\beta\beta$ searches depend on, on the nuclear-data side rather than the matrix-element side.

nucl-ex
Abstract

The cross sections and resonance structures of $\rm^{75}As$(n,$\gamma$)$\rm^{76}As$ reaction are critical to the neutrinoless double-$\beta$ (0$\nu\beta\beta$) decay searches of $\rm^{76}Ge$, the $s$-process nucleosynthesis of nuclear astrophysics, and Neutron Resonance Capture Analysis for determining the elemental and isotopic composition of archaeological and cultural heritage. We report a high-precision measurement of the $\rm^{75}As$ neutron capture cross sections from 1~eV to 1~MeV, performed at the Back-n facility of the China Spallation Neutron Source using the Time-of-Flight method. In the resolved resonance region, nineteen resonance structures of $\rm^{75}As$(n,$\gamma$)$\rm^{76}As$ reaction have been discovered for the first time, and inconsistencies between evaluated libraries has been resolved. Resonance parameters for the newly observed structures were extracted with the $R$-matrix code SAMMY. These findings will help refine the theoretical predictions of half-lives and decay constants for the double-$\beta$ decay searches of $\rm^{76}Ge$. Astrophysical Maxwellian-averaged cross sections were calculated based on the averaged cross sections in the unresolved resonance region. And the $\rm^{75}As$(n,$\gamma$)$\rm^{76}As$ reaction rates were derived over the astrophysically relevant temperature range in both the main and weak $s$-processes nucleosynthesis. The present reaction rates deviate significantly from the recent theoretical predictions, and the uncertainties are significantly reduced.

Jingwei Lian, Jin Min Yang

Inelastic sneutrino dark matter in the inverse-seesaw extension of the NMSSM: approximate lepton-number conservation protects the small mass splitting while the left-handed admixture supplies the inelastic signal. The three-generation completion still reproduces the oscillation observables — an example of the inverse-seesaw sector being used as a model-building resource rather than only as a mass mechanism.

hep-ph
Abstract

We investigate inelastic sneutrino dark matter in the inverse-seesaw extension of the next-to-minimal supersymmetric standard model as an explanation of the high-energy nuclear-recoil candidate reported by LUX-ZEPLIN (LZ). Approximate lepton-number conservation protects the small sneutrino mass splitting, while a left-handed admixture permits an observable inelastic signal with suppressed elastic scattering. Three mechanisms can suppress the solar dark-matter neutrino signal while preserving the thermal relic abundance: annihilation into singlet pseudoscalars with predominantly diphoton decays, thermally enhanced annihilation near a Higgs resonance, and electroweakino coannihilation. We calculate the recoil spectra and confront representative benchmarks with solar-neutrino searches and Fermi-LAT gamma-ray constraints. These experiments stringently constrain the benchmarks, yet we identify points consistent with all the constraints from dark matter, Higgs, and flavour physics considered here. A three-generation neutrino-sector completion can also reproduce the measured neutrino oscillation observables. These results support the viability of the sneutrino interpretation of the LZ event and establish complementary direct and indirect tests of such a supersymmetric model.

Flavour symmetry, GUTs and the strong CP problem2

Ilja Dor\v{s}ner, Mijo Matkovi\'c, Shaikh Saad

Replacing the Georgi-Glashow $24$ with a $75$ fixes gauge-coupling unification outright, with no extra matter invoked for that purpose, and pins the unification scale to $10^{15}\,\mathrm{GeV} \lesssim m_{\rm GUT} \lesssim 10^{16}\,\mathrm{GeV}$ — a window Super-Kamiokande already bites into and Hyper-K will close. The $75$ then admits a unique vectorlike $10_F+\overline{10}_F$ to repair the down-quark/charged-lepton relation, so the fermion sector is far more constrained than in the $24$ case.

hep-ph
Abstract

Breaking of $SU(5)$ down to the Standard Model gauge group can be implemented by any non-trivial self-conjugate scalar representation with a suitable vacuum expectation value. The Georgi-Glashow model accomplishes this breaking with a 24-dimensional representation. That choice, although the most economical one, fails to unify the gauge coupling constants. Moreover, subsequent breaking of the Standard Model down to $SU(3) \times U(1)_\mathrm{em}$ with a $5$-dimensional representation fails to simultaneously provide viable masses for the down-type quarks and the charged leptons. We show that the substitution of the $24$-dimensional representation with a $75$-dimensional representation fixes the gauge coupling unification issue outrightly. We furthermore pin down, by computing the full mass spectrum of the multiplets in $75$-dimensional representation, the range of the unification scale $m_{\rm GUT}$ to be $10^{15}\,\text{GeV} \lesssim m_{\rm GUT} \lesssim 10^{16}\,\text{GeV}$. This unification window is partially excluded by Super-Kamiokande data and will be experimentally accessible at Hyper-Kamiokande. The second issue with the Georgi-Glashow model can be addressed, for example, with vectorlike fermions. The $24$-dimensional scenario admits three different types of vectorlike fermions that can properly account for the mismatch between the down-type quark and the charged lepton masses. The $75$-dimensional scenario, on the other hand, offers enhanced predictivity by allowing only a unique vectorlike addition of $10_F + \overline{10}_F$ that restores realistic charged fermion masses and modestly pushes the upper limit on the unification scale to $m_{\rm GUT} \lesssim 3\times10^{16}\,\text{GeV}$. The proposed framework with $75$-dimensional scalar representation can thus serve as a phenomenologically viable alternative to the standard Georgi-Glashow symmetry breaking paradigm.

Renzhi Su, Minfeng Gu

Constrains $\Delta X/X=(-1.8\pm5.1)\times10^{-6}$ with $X=\mu^{-1}\alpha^{2}g_{p}^{0.54}$ from the four OH ground-state lines toward G035.1+0.5. That combination is exactly the one a unified variation of the gauge and Yukawa sectors at the GUT scale predicts, and the sum-rule method avoids spectral profile fitting, so it survives RFI and scales to SKA volumes.

astro-ph.CO
Abstract

In this paper, we introduce a method to constrain the variation of fundamental physical constants predicted by grand unified theories. This approach utilizes OH sum rules, which exhibit different forms depending on the physical conditions of the OH gas. Employing a least-squares technique, we can directly derive the relative velocity offsets among four OH lines in each ground state. This circumvents the need for spectral profile fitting, which is often unfeasible for spectra with complex profiles. Moreover, this method remains robust even when portions of the spectra are contaminated by radio frequency interference (RFI). Applying this method to a Galactic source G035.1+0.5, we obtained a stringent constraint of $\Delta X/X=(-1.8\pm5.1)\times10^{-6} $, where $X=\mu^{-1}\alpha^{2}g_{p}^{0.54}$. This method is expected to play a crucial role in extracting fundamental physics from large datasets of upcoming Square Kilometre Array (SKA) telescope.

Oscillations and experiments3

Pouya Bakhti, Sudip Jana, Chui-Fan Kong et al.

Solar spin-flavor precession worked out in the full three-active-flavor $6\times6$ Hamiltonian, with the Majorana/Dirac distinction made operational: Majorana transition moments give a lepton-number-violating solar $\bar\nu_e$ signal, Dirac moments only sterile right-handed states and disappearance. No finite-density Majorana crossing survives for normal ordering, but the nonresonant conversion still puts Jinping at $|\mu_{12}|\simeq(2.3-4.1)\times10^{-13}\,\mu_B$, below direct-scattering and stellar-cooling bounds.

hep-phastro-ph.SR
Abstract

We investigate solar-neutrino spin--flavor precession (SFP) induced by magnetic moments in the three-active-flavor framework. For Majorana neutrinos, SFP can convert solar neutrinos into antineutrinos of different active flavors. In the Dirac case, SFP instead produces sterile right-handed states and can lead to the disappearance of active neutrinos. Using the full $6\times6$ Hamiltonians and GS98 and AGSS09 solar profiles, we examine propagation-eigenvalue crossings at $B_\perp=0$ and the projected magnetic couplings between the corresponding states. For normal mass ordering and $1\leq E_\nu/\mathrm{MeV}\leq20$, we confirm the absence of finite-density Majorana crossings. A magnetically coupled Dirac crossing emerges above approximately $12~\mathrm{MeV}$ but involves only a subdominant electron-flavor component, limiting resonant disappearance. Nonresonant Majorana conversion nevertheless offers a distinctive lepton-number-violating solar $\bar\nu_e$ signal, motivating our sensitivity study for the Jinping Neutrino Experiment. For a proposed $3~\mathrm{kt}$ detector operating for five to ten years, we project a 90\% C.L. sensitivity of $P(\nu_e\to\bar\nu_e)\simeq(0.85-1.3)\times10^{-5}$. In the $\mu_{12}$-only benchmark, optimistic solar-core transverse magnetic fields of $B_\perp=7-10~\mathrm{MG}$ imply a reach of $|\mu_{12}|\simeq(2.3-4.1)\times10^{-13}\,\mu_B$, numerically below existing direct-scattering limits and commonly quoted stellar-cooling bounds. This could enable Jinping to provide one of the most stringent projected terrestrial sensitivities to Majorana transition magnetic moments.

Loun\`es Amziane, Soniya Samani, Lorenzo Giannessi et al.

Reparametrizes the superscaling variable $\psi'$ directly in terms of the neutrino-energy reconstruction bias, then expands around the quasielastic point to produce observables built only from outgoing-muon kinematics. The new $L_1$ still separates NEUT, NuWro and GENIE nuclear models across carbon and argon targets — useful if you care how the CCQE model choice propagates into an oscillation fit.

hep-ph
Abstract

In this study, we explore the superscaling variable $\psi'$ within the context of neutrino-nucleus charged-current quasielastic interactions. Building on the neutrino-oriented definition of the superscaling variable $\psi'$, we reparametrize it in terms of the neutrino-energy reconstruction bias, thereby establishing a direct conceptual and analytical connection between the superscaling formalism and neutrino-energy reconstruction. This approach allows the hadronic part of the reconstructed $\psi'$ to be expanded around the quasielastic point, yielding new observables that depend only on the outgoing-muon kinematics. At the same time, the resulting distributions remain sensitive to the underlying nuclear dynamics and vary across nuclear models. Among them, a newly identified quantity $L_1$, constructed solely from the outgoing-muon kinematics, provides a nuclear-physics constraint on the neutrino-energy reconstruction bias. This observable largely inherits the scaling properties of $\psi'$ across different neutrino fluxes and nuclear targets. The nuclear-model dependence is investigated using ND280-like $\nu_\mu$ and $\bar{\nu}_\mu$ Monte Carlo samples on carbon, generated with several nuclear models implemented in NEUT, NuWro, and GENIE, while the stability across experimental conditions is tested using additional carbon- and argon-based flux-target configurations.

D. S. Akerib, A. De Gouvea, P. Elmer et al.

The Division of Particles and Fields' formal input to the SCAC facilities subpanel on DUNE Phase II detectors and U.S. contributions to a future Higgs factory, framed against P5. Short and non-technical, but this is the kind of document that gets cited when the scope of the long-baseline program's second phase is decided.

hep-exhep-lathep-phhep-th
Abstract

The Division of Particles and Fields (DPF) of the American Physical Society would like to thank SCAC for providing an opportunity for input to the SCAC facilities subpanel. The DPF represents scientists working at U.S. Universities and DOE Laboratories on understanding fundamental particles and forces. We are focused on Discovery Physics. The subpanel has been asked to consider two proposed DPF-related projects, the DUNE Phase II Detectors and supporting infrastructure and U.S. contributions to a future Higgs Factory. In this note, we briefly describe the questions driving our field and the P5 strategic plan and other community prioritization documents that form the backbone of our comment. The following sections provide short descriptions of the two projects, highlighting information relevant to your charge, answers to your specific questions, and a description of the process that produced this note.

Astroparticle physics and cosmology1

Bao-Jun Cai, De-Qing Fang, Yu-Gang Ma

A review of how the neutron skin propagates into heavy-ion emission observables and the density dependence of the symmetry energy. The relevant hook is the section tying it to parity-violating electron scattering and coherent elastic neutrino-nucleus scattering: the same isovector density profile controls the CE$\nu$NS form-factor systematics that limit NSI extractions.

nucl-thastro-ph.HEhep-phnucl-ex
Abstract

The neutron skin, defined by the difference between neutron and proton root-mean-square radii, is a characteristic manifestation of isospin asymmetry and an important probe of the isovector nuclear interaction. This focused review examines how neutron skins influence particle emission and collective dynamics in heavy-ion collisions, from the Fermi-energy regime to ultra-relativistic energies. By modifying the initial neutron and proton density profiles, the neutron skin affects the isospin composition and geometry of the participant region, pre-equilibrium emission, particle production, fragment formation, and collective flow. We review neutron-to-proton and $\rm{t}/^3\rm{He}$ yield ratios, light clusters, pion ratios, bremsstrahlung photons, isoscaling and fragment momentum distributions, and neutron-proton differential flow and momentum observables, emphasizing their interplay with the symmetry energy and transport dynamics. At high energies, neutron skins also modify the initial geometry, eccentricities, multiplicities, and anisotropic flows in isobar and heavy-nucleus collisions. We discuss the challenge of disentangling these effects from deformation, surface diffuseness, shell structure, clustering, and model dependence. Broader connections to parity-violating electron scattering, dipole responses, coherent elastic neutrino-nucleus scattering, SRC-induced proton skins in momentum space, and neutron-star observables are also explored. Finally, we highlight opportunities from radioactive beams, improved collision experiments, microscopic many-body and transport calculations, and Bayesian inference. Combining multiple reaction systems and observables with complementary nuclear-structure and astrophysical information will be essential for quantitatively constraining neutron skins and the density dependence of the symmetry energy.

Other relevant work1

Jianlong Lu

Matter potentials and off-diagonal NSI enter the flavor-basis Hamiltonian as a low-rank additive deformation, and this constructs the full ring of quantities insensitive to it — with an exact dimension formula for arbitrary flavor number. The sharp statement for $3+1$: the eleven invariants in common use are a generic local coordinate system, not a global polynomial generating set, the global object being the toric cycle ring of the four-vertex flavor graph.

hep-ph
Abstract

Matter changes the eigenvalues and mixing matrix of the neutrino propagation Hamiltonian while entering the flavor-basis Hamiltonian through a low-dimensional additive deformation. We develop a unified algebraic description of the quantities that are insensitive to this deformation. The invariant algebra is formulated as the joint kernel of commuting matter-translation derivations inside the flavor-rephasing invariant ring. For diagonal matter potentials, this gives a general decomposition into unaffected diagonal directions and an off-diagonal cycle algebra, together with an exact dimension formula for an arbitrary number of flavors and independent matter parameters. For matter spurions with common low-rank support, block-Krylov rows generate exterior-power covariants whose maximal minors are matter independent. Their mass-basis form is a Pl\"ucker expansion: rank one produces the familiar Vandermonde factorization, whereas higher rank generically produces a sum of independent Pl\"ucker terms. The standard $3+1$ system provides our principal nontrivial example. Its global off-diagonal algebra is the toric cycle ring of the complete four-vertex flavor graph, generated by edge moduli, triangle cycles, and quadrangle cycles; the commonly used eleven invariants constitute a generic local coordinate system rather than a global polynomial generating set. We further formulate independently varying matter compositions and off-diagonal nonstandard interactions as, respectively, commuting exact flows and controlled deformations of the invariant algebra. This framework separates the existence of exact invariants from the stronger and exceptional property of single-monomial spectral factorization.

Bonus — unexpected connections

Cetin Hakimoglu-Brown

Fricke transformations are the same objects that stabilize the modulus at the self-dual point in modular flavor models; here they organize two-term Rogers dilogarithm identities for rank-two Nahm sums, and the cusp growth of the index-13 system reproduces the saddle action with all three leading Fricke amplitudes exact.

math.NT
Abstract

We study the arithmetic constraints that two-term Rogers dilogarithm relations impose on rank-two Nahm systems with mixed denominator steps. Monomial complement equations give a uniform conversion to quadratic data in every algebraic degree. Within a specified ten-record simplest-cubic family, positive coupling, positive definiteness, and integer-valued exponents leave, for m > 2, exactly the steps (1,3), (1,13), and (1,31). At the smallest compatible modulus 31, the required support cannot be a multiplicative subgroup coset. Quadratic examples include known product identities and two systems for which the first radial correction excludes every individual modular sum with rational linear terms. For the index-13 system, we prove a two-term Rogers identity and recover its arguments from the matrix of a previously proved two-dimensional Fricke transformation. Its cusp growth agrees with the resulting saddle action, and an independent calculation reproduces all three leading Fricke amplitudes exactly. The associated two-summand product evaluations remain conjectural; the small rank and dimension contrast with the classical rank-five, six-component Andrews-Gordon construction at the same modulus. A mixed-signature cubic family illustrates the limits of the arithmetic restriction

Eran Assaf, Madeline Brandt, Juliette Bruce et al.

Level-$m$ structures on principally polarized abelian varieties are the congruence subgroups whose quotients give the finite modular flavor groups $\Gamma_N$. Seeing the tropicalization $A_2[m]^{\rm trop}$ computed explicitly — a wedge of orientable surfaces and circles, with genera counted — is a concrete picture of what level structure does near the cusp.

math.AGmath.CO
Abstract

We introduce level structures on tropical abelian varieties and give a modular interpretation of $A_g[m]^{\mathrm{trop}}$, the tropicalization of the moduli space $\mathcal{A}_g[m]$ of principally polarized abelian varieties with level $m$ structure. We study the case of abelian surfaces in greater depth. The link of $A_2[m]^{\mathrm{trop}}$ is an explicit simplicial complex whose vertices are the primitive vectors of $(\mathbb{Z}/m\mathbb{Z})^4$ up to sign. As a topological space, this link is homotopic to a wedge sum of closed orientable surfaces and circles; we compute the number of each of these and the genera of the surfaces. We deduce the weight zero compactly supported rational cohomology of $\mathcal{A}_2[m]$, completing a calculation of Oda-Schwermer from 1990.

Source note. export.arxiv.org refused this machine all morning: across two full runs with exponential back-off, the API returned HTTP 429 or timed out on hep-ph, hep-ex and hep-lat until the retry budget ran out, and only hep-th ever answered. The candidate set below therefore comes from the per-category RSS feeds on rss.arxiv.org, a different host with its own rate limiter, which answered normally: all 15 categories were retrieved and none is missing from the scan , so no subject area is under-represented here — only the transport changed. Two consequences follow from that change. First, the unit is an announcement rather than a submission window: Tuesday’s announcement carries submissions received between Friday 14:00 ET and Monday 14:00 ET, which is the weekend batch that Monday’s edition could not yet contain. Second, RSS items carry no submission timestamp, only the announcement date, so every entry above is dated by announcement. No paper here appeared in the edition of 14 September; the identifier ranges do not overlap.