11 September 2026

Recent developments in the Swampland program motivate the existence of a mesoscopic Dark Dimension of size $0.1-10~μ$m with bulk Majorana fermions in the $1-10$ keV range. Motivated by this, we derive terrestrial constraints on Majorana bulk neutrinos as a function of the compactification radius. After determining the mass spectrum and mixing structure, we confront the model with Daya Bay neutrino-oscillation data, the KATRIN beta-decay bound, and the KamLAND-Zen neutrinoless double beta decay limit. For the latter, we obtain a closed-form expression for the effective Majorana mass and show that the Kaluza-Klein tower efficiently screens neutrinoless double beta decay when the nuclear momentum exceeds the compactification and Majorana scales. In the Dark-Dimension window, beta decay provides the strongest constraint, pushing the allowed Yukawa couplings down to $\mathcal{O}(10^{-3})$. Oscillation and neutrinoless double beta decay searches remain complementary, probing smaller and larger Majorana masses, respectively. For completeness, outside the Dark-Dimension assumptions, we investigate how hierarchical Majorana masses can weaken the constraints.

We construct canonical chiral $\mathcal N=(0,1)$ sigma models on Spin(7) manifolds. The Spin(7) structure fixes the rank-seven bundle of the left-moving fermions, whose quadratic index matches the tangent representation, so the internal anomalies cancel while the rank difference leaves the gravitational anomaly of one right-moving Majorana--Weyl fermion. A transverse section of the left-moving bundle has a 1D zero locus with induced String structure, and we compute its class in the first torsion group of topological modular forms. The class is nonzero precisely when the Euler characteristic of the target is odd. The standard Joyce action on the torus has no internal finite-group anomaly and can be gauged to define an exact chiral spin QFT. We show that the orbifold Euler characteristic is even throughout the diagonal Joyce family generated by coordinate reflections and half-shifts preserving the Cayley form. By contrast, a free antiholomorphic quotient of the Fermat sextic is a compact torsion-free Spin(7) target with Euler characteristic 1305 and realizes the nonzero class.

We identify the precise F-theory backgrounds dual to the heterotic string theory compactified on $T^2$ with general Wilson lines turned on for one of the two $E_8$'s. The elliptic curve describing the backgrounds is expressed in terms of orthogonal modular forms and is determined so that it admits a nontrivial scaling limit yielding a rational elliptic surface. We confirm that the curve reduces to the Seiberg-Witten curve for the E-string theory in this limit. We conjecture that our result gives an explicit inverse period map for algebraic K3 surfaces polarized by the $U\oplus E_8(-1)$ lattice.

The $\mathcal N=1$ superconformal minimal model with $m=12$ and the exceptional modular invariant $(E_6,D_8)$ is the unitary minimal model of the super-$W_3$ algebra. We propose its Landau-Ginzburg description using two real scalar superfields with the cubic superpotential ${\cal W}=g_1 XY^2/2 + g_2X^3/6$. For $g_1=g_2$, this superpotential is known to describe a product of two $m=3$ $\mathcal N=1$ superconformal minimal models, which is the $m=10$ model with the $(D_6,E_6)$ modular invariant. The exceptional $m=12$ superconformal minimal model is realized at a different fixed point of the same theory. Testing this Landau-Ginzburg description requires the fusion ring of the minimal model, which we obtain from the modular data of the extended algebra. The fusion ring has a $\mathbb Z_2$ grading by chiral fermion parity that the ordinary fusion coefficients do not determine. This grading, composed with conjugation, gives the generator of the R-parity $\mathbb Z_2^{R}$ of the Landau-Ginzburg theory. We then treat the theory with superpotential $\cal W$ as a Gross-Neveu-Yukawa model in $d=4-ε$ and find a weakly coupled infrared fixed point with $g_1/g_2=3/2+\mathcal O(ε)$, at which supersymmetry emerges. We also describe the renormalization group flow from this fixed point to the decoupled fixed point with $g_1=g_2$. The operator dimensions at the coupled fixed point, continued to $d=2$, agree approximately with their values in the $m=12$ superconformal minimal model. Finally, we estimate the scaling dimensions in the new interacting $d=3$ $\mathcal N=1$ superconformal field theory.

We study the representation theory of the vertex operator algebras (VOAs) associated with rank-one 4d $\mathcal{N} = 3$ superconformal field theories. For the $\mathbb{Z}_3$ S-fold theory, whose VOA $\mathcal{W}_{\mathbb{Z}_3}$ has central charge $c_{\mathrm{2d}} = -15$, we use the $\mathcal{N} = 1$ Lagrangian description to obtain the unflavored Schur index in terms of Dedekind eta functions, while Wilson-loop indices yield the unflavored non-vacuum characters. These characters all solve a modular linear differential equation (MLDE) whose solution space also contains a logarithmic character. Combining flavored MLDEs from null states with Zhu's associative algebra and a free-field realization, we study four highest-weight modules of $\mathcal{W}_{\mathbb{Z}_3}$ and their flavored characters in closed form. A parallel analysis applies to the $\mathcal{N} = 3$ theories obtained by gauging a discrete $\mathbb{Z}_n$ flavor subgroup of $\mathcal{N} = 4$ $U(1)$ and $SU(2)$ super-Yang--Mills, for which we also obtain closed-form Schur indices and a new free-field realization of the VOA of the $\mathbb{Z}_4$ quotient.

NOvA is a long-baseline neutrino oscillation experiment designed to study the neutrino mixing parameters, mass ordering, and CP violation in the lepton sector. A key component of the success of the experiment is a robust understanding of the systematic uncertainties associated with detector response and calibration. To address this, NOvA deployed a Test Beam experiment at the Fermilab Test Beam Facility, which collected data from April 2019 through July 2022. The NOvA Test Beam experiment used a 30-ton segmented liquid scintillator detector functionally identical to the NOvA Near and Far Detectors to analyze tagged particles produced from p-Cu collisions, with instrumentation capable of selecting and identifying electrons, muons, pions, kaons, and protons with momentum ranging from 0.4-1.5GeV/c. Analysis of the collected data provides a better understanding of the largest systematic uncertainties impacting NOvA's analyses, which include the detector response, energy calibration, and hadronic and electromagnetic energy resolutions.

Naive estimates based on Einstein gravity with Lagrangian $\frac{1}{2}M_{pl}^{2}(R-2Λ)$ suggest that, if the radiation era extended back to the Big Bang (i.e., as far back as the classical spacetime background makes sense), this would result in an over-production of dark matter and a relic cosmic background of thermal gravitons. Here we revisit these conclusions in quadratic gravity, the minimal renormalizable completion of Einstein gravity, whose Lagrangian also includes the terms $\frac{1}{6}f_0^{-2}R^2-\frac{1}{2}f_{2}^{-2}C^{2}$. Assuming the radiation era does extend back to the bang, we find a novel relation between the coefficient $f_{2}$ and the dark matter mass $m_{dm}$, needed to obtain the correct dark matter abundance. This yields a new gravitational production mechanism for dark matter (e.g., stable right-handed neutrinos). Moreover, the presence or absence of the relic graviton background (detectable by forthcoming CMB experiments via its small imprint on $N_{\rm eff}$) will place new constraints on $f_{0}, f_{2}$.

While still under construction, the KM3NeT Astroparticle Research with Cosmics in the Abyss (ARCA) detector recorded a $\sim$200 PeV neutrino on February 13th, 2023. This event is the highest-energy neutrino reported. IceCube, a cubic kilometer neutrino detector located at the geographic South Pole, has previously detected neutrinos up to approximately 10 PeV. We search for high-energy neutrinos from the location of the KM3NeT event using 15 years of IceCube data and considering three temporal hypotheses: steady or flaring in time coincidence, or at an arbitrary time. We find no evidence for neutrino emission for any of the studies performed. Correspondingly, we set upper limits on the neutrino flux from a point source in the direction of KM3-230213A. We compare these limits to KM3NeT's estimated flux and show that an astrophysical explanation of this event is strongly constrained for a variety of spectral assumptions for a steady or transient point source with the flux inferred from the single KM3NeT ultra-high-energy event assuming a spectral index of 2.0.

The LUX-ZEPLIN (LZ) Collaboration recently reported the detection of a single nuclear recoil candidate event with a very high recoil energy. The lack of any corresponding low-energy events motivates models in which dark matter scattering with nuclei has a nontrivial momentum dependence or proceeds inelastically, suppressing the rate of low-energy recoils. In this study, we consider the constraints on inelastic dark matter, including scenarios favored by the LZ event, from the absence of an excess of high-energy neutrinos from the Sun in IceCube observations. We confirm the results of Pospelov & Ramani and show, more generally, that the lack of an excess of high-energy neutrinos from the Sun strongly constrains the parameter space in this class of models.

The recent observation of a 220 PeV neutrino event (KM3-230213A) by the KM3NeT observatory presents a formidable challenge to standard astrophysical source models. We investigate the hypothesis that this ultra-high-energy signature originates from the terminal evaporation burst of a Primordial Black Hole (PBH). Since PBH evolution spans cosmic history, static vacuum approximations fail to capture early-universe dynamics. Embedding the PBH in a cosmological background via the McVittie spacetime, we demonstrate that early-universe cosmological accretion and expansion-suppressed Hawking emission shift the required initial mass window for a terminal burst occurring today. We show that although the early universe environment dictates the black hole's overall lifespan, its final explosion today ($z \approx 0$) is governed by standard Schwarzschild thermodynamics. This mechanism naturally produces the intense 220 PeV local flux while suppressing early emissions, thereby satisfying diffuse isotropic background limits. Consequently, this dynamical framework alters the mapping between current ultra-high-energy neutrino observables and the primordial curvature perturbations that seeded them.

We study the inelastic dark matter (iDM) that consists of two-component dark matter particles $(χ_1,χ_2)$ and serves as a minimal extension beyond the commonly used one-component DM models. A distinctive feature of such iDM scattering with the target nuclei is to favorably produce signals at high nuclear recoil (NR) energy region in both exothermic and endothermic processes. In particular, for the exothermic dark matter scenario, the signal does not rely on the tail of the Boltzmann velocity distribution. As a result, the required DM-nucleus scattering cross section is significantly reduced, which in turn helps to substantially relax the stringent constraints imposed by IceCube neutrino searches. Using the inelastic DM-nucleus scattering, we naturally explain the newly reported event excess at high recoil energy with the LUX-ZEPLIN (LZ) experiment.

We investigate non-invertible selection rules originating from the discrete $H$-gauging of theories with an underlying discrete global symmetry group $G$. To systematically describe these theories, we formulate a general framework for $H$-gauged models that incorporates generalized field transformations. Our approach naturally accommodates non-Abelian groups, for which multidimensional irreducible representations play an essential role. In such models with non-Abelian groups, the transformations induced by $H$ non-trivially mix the internal components of $G$-multiplets, potentially projecting out specific degrees of freedom. Consequently, conventional selection rules based on standard tensor product decompositions or conjugacy classes become insufficient. By analyzing the full semidirect product $G \rtimes H$, we introduce projected characters to derive necessary and sufficient conditions for non-vanishing $n$-point bare couplings. Furthermore, we demonstrate that the remaining field components obey an associative fusion-like algebra governed by their Clebsch-Gordan coefficients. Phenomenologically, these selection rules restrict allowed interactions and impose specific relations among coupling constants. We illustrate our results through concrete examples, including $Δ(54) \cong Δ(27)\rtimes \mathbb{Z}_2$ and $S_4 \cong A_4 \rtimes \mathbb{Z}_2$.

We study the restricted fan cut inside the dual fundamental Weyl chamber by the weights of a $27$-dimensional minuscule representation of $E_6$; the two such representations are dual and give the same arrangement. Only $11$ of the $27$ weights have kernels meeting its interior, and we prove that they determine the entire fan. It has exactly $14$ chambers and $18$ extreme rays, every chamber is a six-dimensional simplicial cone, and we determine all facets, rays, and incidence relations. The chamber count was previously obtained by Diaconescu and Entin; the simplicial structure, extreme rays, and incidence data are new. The geometry of the $27$ lines on a cubic surface then explains and organizes the resulting chamber architecture. We also enumerate all faces, compute both characteristic polynomials---the arrangement is not supersolvable---together with lattice indices and projective chamber volumes, and describe the oriented matroid. Our main result is representation-theoretic. A distinguished $14$-element visible subposet of the minuscule $\mathbf{56}$ of $E_7$, defined entirely inside $E_7$, has Hasse diagram equal to the chamber adjacency graph of the $E_6$ arrangement. Three canonical $7+7$ splittings of it, of types $A_7$, $D_7$, and $E_7$, are the visible traces of Levi-center $\mathfrak{u}(1)$-charge decompositions of the $\mathbf{56}$ and reproduce the three level-$8$ decompositions on the $E_6$ side. More strongly, the simple-root labels on its covers, transported by minimal-length coset representatives, recover chamber by chamber all six facets and, globally, the $11$ active weight hyperplanes and the boundary walls of the dual Weyl chamber. Thus the $E_7$ shadow records not merely the chamber graph but, once matched with the independent $E_6$ classification, the full local wall architecture of $I(E_6,\mathbf{27})$.