25 August 2026

The dynamics of particles in the early universe are described by Boltzmann equations, which involve high-dimensional phase-space integrals. Classical approaches use quadrature integration and evolve the system on a fixed momentum grid, which scales poorly to complicated systems and parameter scans, severely limiting the complexity of processes that can be studied. We introduce Neural Boltzmann Equations (NBEs), which combine three coupled concepts to overcome these limitations. First, particle properties are encoded in physics-inspired neural distribution functions, with parameters that can be predicted using neural networks, enabling efficient parameter scans. Second, phase-space integrals are evaluated with Monte Carlo, using importance sampling tools from collider physics. Third, we use the natural gradient method to evolve the system. After demonstrating the individual benefits of NBEs, we use the framework to perform a precision calculation of the effective number of relativistic neutrino degrees of freedom in the early universe.

Extensions of the Standard Model by a $U(1)_{X}$ gauge symmetry predict a new $Z'$ boson, whose mass is severely constrained by high-mass dilepton resonance searches at the LHC. We show that these bounds can be relaxed by generalizing the chiral $(B-L)$ charge assignment while preserving gauge anomaly cancellation. The resulting $U(1)_X$ charges are parameterized by two independent parameters, and an appropriate choice of these parameters suppresses the $Z'$ branching fraction into charged leptons, substantially weakening the dilepton constraints. The framework accommodates Dirac neutrino masses through a Dirac type-I seesaw mechanism and a stable singlet scalar DM candidate without requiring an additional discrete symmetry. We find that the modified charge assignment, although beneficial for collider phenomenology, introduces a tension between obtaining the observed relic abundance and satisfying direct detection limits when DM annihilation proceeds solely through the $Z'$ portal. The inclusion of scalar-mediated annihilation channels resolves this tension and opens up a broad viable parameter space, with DM masses ranging from $M_{\rm DM}\simeq 60~{\rm GeV}$ to $10~{\rm TeV}$. The resulting parameter space is consistent with the observed relic density, direct detection, collider, and electroweak precision constraints, demonstrating that a generalized chiral charge structure can simultaneously accommodate a less constrained $Z'$ sector, neutrino masses, and viable dark matter phenomenology.

We present a search for the lepton-flavor-violating decay $τ^{\pm}\toμ^{\pm}γ$ using a data sample that corresponds to an integrated luminosity of 428 fb$^{-1}$ recorded by the Belle II experiment at the SuperKEKB asymmetric-energy $e^{+}e^{-}$ collider. We employ a multivariate classifier to suppress the backgrounds from the Standard Model processes, and the signal extraction is performed using an extended maximum-likelihood fit. Since no significant excess over the expected background is observed, we set an upper limit on the branching fraction $\mathcal{B}(τ^{\pm}\toμ^{\pm}γ) < 9.5$ $ (12.2)\times10^{-8}$ at the 90\% (95\%) confidence level, using the CL${_s}$ technique.

We study perturbative anomaly inflow for effective theories supported on orbifold fixed loci of the internal geometry. Donnelly's equivariant APS theorem gives a fixed-point density, whose degree-\((d+2)\) component is identified as the anomaly polynomial of the \(d\)-dimensional effective theory. We apply the construction to six-dimensional A-type orbi-instanton theories engineered by \(N\) M5-branes probing a transverse \(\mathbb{C}^2/\mathbb{Z}_k\) singularity at an end-of-the-world M9-brane. For a flat \(E_8\) connection specified by \(ρ:\mathbb{Z}_k\to E_8\), we compute the non-identity ALE fixed-point class on the M9 wall. Its degree-eight component agrees with the complete Kac-label-dependent remainder conjectured in \cite{MOTZ}, including the \(SU(2)_R\) and tangent-bundle curvatures. Together with the known M5/Hořava--Witten and ALE/Hořava--Witten terms, this reproduces the unflavored tensor-branch anomaly polynomial. This local equality further suggests a complete M-theory corner-inflow interpretation. The same prescription also be extended to include flavor symmetries as the centralizer of \(E_8\).

Motivated by the old idea of treating gravity as a gauge theory, we review the gauge-theoretic construction of Conformal Gravity and of Noncommutative (Fuzzy) Gravity. We then outline how these gauge formulations of gravity can be unified with internal interactions described by an SO(10) Grand Unified Theory, based on the critical observation that the dimension of the tangent-space symmetry group of a curved manifold need not coincide with the spacetime dimension.

We explore a unified axion framework connecting grand unification, string-inspired axion-like particles (ALPs), and cosmology. Starting from the QCD axion associated with Peccei--Quinn symmetry in supersymmetric SO(10) GUT, we consider the broader spectrum of ultralight ALPs motivated by heterotic string theory. Within this multi-axion structure, we focus on two ultralight scales selected by cosmological requirements. A mode of order $10^{-22}$ eV is assumed to constitute the dominant dark-matter component and can form a Bose--Einstein condensate whose attractive self-interaction leads to nonlinear collapse, providing possible seeds for high-redshift supermassive black holes. A lighter eigen-direction with a characteristic dynamical scale of order $10^{-28}$ eV can transiently increase the pre-recombination expansion rate and reduce the sound horizon. An order-of-magnitude estimate shows that addressing the Hubble tension requires a sound-horizon-weighted axion fraction of order 0.1, corresponding, for a large initial displacement, to an effective decay constant of order $10^{18}$ GeV. We show that a multi-axion--multi-instanton system can in principle provide both the required aligned light direction and a higher-order effective potential that makes the $10^{-28}$ eV contribution transient. The framework links theoretically motivated axionic degrees of freedom to the distinct scales required by dark-matter, early-black-hole, and Hubble-tension phenomenology.

The five-dimensional Minimal Supersymmetric Standard Model (5D MSSM) provides an attractive framework in which power-law renormalisation group evolution naturally generates a sizeable trilinear stop coupling, allowing the observed Higgs boson mass to be reproduced without requiring too heavy a supersymmetric spectra. In this work we present a comprehensive two-loop analysis of the 5D MSSM, deriving the complete renormalisation group equations governing the gauge, Yukawa and soft supersymmetry-breaking sectors and examining the perturbative consistency of the theory. Particular attention is given to the ultraviolet behaviour of the model, where we demonstrate that the potentially dangerous leading two-loop contributions cancel as a consequence of the underlying $\mathcal{N}=2$ supersymmetry, leaving a well-behaved perturbative expansion. Building upon this framework, we compute the radiatively corrected Higgs effective potential including the complete Kaluza-Klein (KK) contributions through KK resummation, and investigate the resulting implications for the Higgs sector. The phenomenological viability of the model is subsequently explored through detailed numerical studies of the Higgs boson mass, electroweak precision observables, Higgs coupling modifiers and signal strengths, allowing constraints on the compactification scale and supersymmetric parameter space to be established. We find that the inclusion of the two-loop corrections preserves the characteristic power-law behaviour of the five-dimensional theory while yielding a phenomenologically viable parameter space consistent with current collider and precision measurements.

We give a local newform theory for the metaplectic group of rank 1 over a non-archimedean local field of characteristic 0 with odd residual characteristic. It was suggested by some results of Kohnen and Ueda on the classical theory of modular forms of half-integral weight.

Ultra-high-energy (UHE) neutrinos, with energies above $100\,\mathrm{PeV}$, are powerful probes of fundamental physics, offering unique opportunities to test and constrain models beyond the Standard Model. A central challenge is achieving sensitivity to their flavor composition, which encodes information about production mechanisms at the source as well as potential new physics during propagation. We propose, for the first time, a three-technology strategy to measure the flavor composition of UHE neutrinos by leveraging the complementary strengths of planned and existing experiments. This approach integrates in-ice radio (ARA, ARIANNA, RNO-G, the IceCube-Gen2 radio array), Earth-skimming (TAMBO, POEMMA, Trinity, AUGER, GRAND200k), and in-ice optical Cherenkov detectors (the IceCube-Gen2 optical array). We demonstrate the potential to achieve unprecedented sensitivity to UHE neutrino flavors. The method can be used to probe an energy-dependent neutrino flavor transition at the source across energies ranging from TeV to EeV. As such, this article highlights the discovery potential of a coordinated, multi-technology program for advancing both high-energy and ultra-high-energy neutrino astrophysics.

We present a simple model with a n + 4-dimensional metric with compactified extra dimensions with a space dependent radius R. We show that changes in the profile of R are sourced by (visible) matter density and Newtonian potential. We can reproduce rotation curves of spiral galaxies and provide an expression for R. In order to test our hypothesis, we propose six experiments.