Papers

The symmetric Macdonald polynomial at peculiar values of parameter $t=q^{-m}$, $m\in\mathbb{Z}_{\ge 0}$ is naturally split into non-symmetric parts, which are the (quasi)polynomial Baker-Akhiezer (BA) functions. One may think this is due to symmetricity, and one just picks up this way non-symmetric parts already containing all the information. However, we demonstrate that, in the case of non-symmetric Macdonald polynomials, it still works, though each single BA function splits into $N!$ distinct (quasi)polynomial BA functions. The sum of these functions gives rise to the universal solution of the eigenstate problem for the Cherednik Hamiltonians. Extending to arbitrary values of $t$ is also immediate giving rise to counterparts of the Noumi-Shiraishi power series. Altogether, this power series and its reductions to non-symmetric Macdonald polynomials and to BA functions form a non-symmetric triad. There are $N!$ different branches of the non-symmetric triad, each branch being split into $N!$ distinct triads, and of these $(N!)^2$ triads $N!(N-1)!$ are independent. We describe in detail the simplest $N=2$ case.

We investigate the feasibility of precision counting experiments based on laser-electron beam interactions to verify strong-field quantum electrodynamic effects, with particular emphasis on the stochastic nature of photon emission, photon polarization, and spin asymmetry. A precise Monte-Carlo model is developed using photon packets with multi-dimensional phase-space weighting, hierarchical-mesh cumulative distribution functions, and a variable time-step method. This model quantitatively reproduces the highest edge of the photon energy spectrum and the positron yield in the previous SLAC E-144 experiment. The quantized radiation back-reaction determines the highest edge tail and thus the positron yield for higher laser intensities. The spin asymmetry in photon emission and spin flip determines photon polarization in the high-energy tail, while that in pair production can be observed through the large-angle positron scattering. Our simulations predict that these effects depend on the combination of the electron-beam energy and the laser intensity, and that they could be verified in future ELI-NP experiments using sub-GeV electron beams and optical lasers with intensities ~10^22W/cm2.

We study gravitational-wave production during perturbative reheating without assuming instantaneous thermalization of the inflaton decay products. The injected energetic particles thermalize through an in-medium cascade of nearly collinear splittings subject to the Landau-Pomeranchuk-Migdal effect and are ultimately isotropized by elastic scatterings near the thermal scale. The non-thermal hard population present before complete thermalization produces an additional gravitational-wave component through hard-soft scatterings, with $\Omega_{\mathrm{GW}}\propto f^{1/2}$ below the injection-scale turnover. The same isotropization erases the directional information underlying the vacuum $1/k$ bremsstrahlung soft pole, changing the deep-infrared spectrum from $\Omega_{\mathrm{GW}}\propto f$ to $\Omega_{\mathrm{GW}}\propto f^3$.

We consider three specific $q$-deformed matrix models (the Chern-Simons, $q$-Laguerre, and $q$-Gaussian matrix models) which can be solved explicitly using the property of superintegrability. We show that one- and two-point functions of inverse characteristic polynomials can be interpreted as quantizations of Lagrangian subvarieties in $(\mathbb{C}^*)^2$ and $(\mathbb{C}^*)^4$, respectively. While such a geometric picture is expected for the Chern-Simons matrix model, our results for the $q$-Laguerre and $q$-Gaussian models are new and exhibit additional features. In particular, specific anti-symplectic birational involutions play an essential role in the construction. This reformulation provides a geometric framework for analyzing the semiclassical, large-$N$ expansion of matrix-model correlators. This picture is suggestive of the geometry underlying open topological strings, although the two constructions are not identical and the precise relation between them remains to be understood.

We study the scattering of massless scalar waves by static black holes embedded in dark matter halos. The halo is modelled by means of a Hernquist profile, for which the Einstein equations admit an exact solution. We analyse the scattering using null geodesics, the glory approximation, the partial wave expansion, and the complex angular momentum (CAM) method. The geometric analysis shows that the presence of the halo changes the light ring radius weakly but shifts the critical and glory impact parameters. The wave analysis shows that the characteristic black hole interference pattern is preserved, with halo compactness providing the leading correction and the halo scale radius playing a secondary role. For sufficiently compact halos, the environment also induces a sizeable gravitational redshift. Most of the displacement of the interference extrema can be reproduced by a vacuum Schwarzschild solution with an appropriately chosen $\omega M_{\rm BH}$. A non-vanishing residual, however, reveals a genuine halo contribution that cannot be absorbed into such an effective frequency shift. Finally, we perform the CAM reconstruction of the scattering cross section and find that only a few Regge poles are required to achieve high accuracy at large angles.

We construct a two-scalar hairy planar black hole in four-dimensional Einstein gravity coupled to two scalars whose potential descends from the ABJM consistent truncation of eleven-dimensional supergravity. Starting from the known single-scalar hairy black brane, we switch on the second scalar $\phim$ perturbatively in its dimensionless hair parameter $\eps$, which at fixed source is proportional to $\lambda_{-}T$, and solve the coupled Einstein-scalar system to order $\eps^{2}$. The linearized $\phim$ profile is an exact hypergeometric function, independent of the $\pp$ hair, whose horizon-regular branch always carries a source, so there is no spontaneous $\phim$ hair. Because the dual operator is irrelevant ($\Delta_{-}=4$), the second-order response develops a resonant logarithm: the condensate runs with a closed-form coefficient fixed by the cubic vertex. The metric and $\pp$ back-reaction is obtained in closed form; for arbitrary hair it diagonalizes into two Pöschl-Teller problems and locks the $\pp$ correction to the transverse metric correction with ratio $6/\sqrt7$. On AdS-Schwarzschild the first law and holographic renormalization agree and give an analytic equation of state, $T/T_{0}-1=-\tfrac{5\sqrt3}{8\pi}\eps^{2}$ at fixed entropy and $c_{s}^{2}=\tfrac12-\tfrac{5\sqrt3}{8\pi}\eps^{2}$, with $\eta/s=1/4\pi$ and $\zeta/\eta=\tfrac14\eps^{2}$. We then add the $\mathbb{Z}_{2}$-odd third scalar $\chi$ of the truncation, dual to $\Delta_{\chi}=5$. On the hairy background its linear equation is a Heun equation with an apparent singularity, solved by a Clausen function. At second order $\chi$ necessarily sources $\phim$, yet neither cross-coupling makes either condensate run, a mutual non-renormalization that follows from a one-step resonance identity and the relation $2\Delta_{\chi}-\Delta_{-}=2d$.

Large primordial curvature and tensor perturbations on small scales can generate second-order tensor-scalar induced gravitational waves (TSIGWs) through scalar-scalar, tensor-scalar, and tensor-tensor source terms. TSIGWs are recognized as one of the principal contributors to the stochastic gravitational wave background (SGWB) observations. We explore the energy density spectrum of second-order TSIGWs in the presence of non-Gaussian primordial curvature perturbations. Furthermore, we present the first calculation of the anisotropic angular power spectrum associated with second-order TSIGWs, which provides a promising tool to discriminate them from other SGWB sources.

We study the production of $c$ and $b$ quarks in photon-induced processes as a probe of gluon saturation, with a focus on the high-energy region accessible in ultra-peripheral collisions (UPCs) at the LHC. We compare predictions for inclusive and diffractive heavy quark production with and without saturation effects by using the nonlinear Balitsky–Kovchegov and the linear Balitsky–Fadin–Kuraev–Lipatov equations for the evolution of the dipole amplitude. The percentage of coherent diffractive events is predicted to be $~20\%$ in the saturation model, which is approximately twice as large as predictions based on parton distribution functions and shadowing. This indicates that measurements of diffractive heavy quark production in UPCs may provide a sensitive probe for distinguishing linear and nonlinear regimes of quantum chromodynamics.

In this paper, we build the Galilean limit of the free Kalb-Ramond two-form and also study the symmetries. Two different methods are discussed. The first is an Inönü-Wigner contraction. In this method, we take the scaling of space-time coordinates and the two-form field. The relativistic equations boil down to two inequivalent limits, electric and magnetic. In both, the equations of motion come out to be invariant under the full infinite-dimensional Galilean conformal algebra precisely in D=6. The second method is the null-reduction. In this, we start from a theory in D+1 dimensions and end up with a theory in D dimensions. This method yields a local Galilean Lagrangian. Here, the action is invariant under the global generators (boosts, rotations, translations and scale transformations) but not under higher Witt modes of the Galilean conformal algebra. We also calculate the two-point functions in both constructions from the boost, scale and rotation Ward identities, and by exhibiting the truncation that maps the null-reduction correlators onto those of the magnetic limit.

We establish the general form of the evolution equation and study scattering and tunneling in real quantum mechanics. We prove an analogue of Stone's theorem for a real Kahler space and derive the corresponding general evolution equation, whose evolution operator is both orthogonal and symplectic. We formulate scattering theory in terms of real wave operators and the associated S-matrix. For the class of potentials considered, we show that the differential scattering cross section is equivalent to that obtained in standard complex quantum mechanics. We also show that the tunneling probability in real quantum mechanics is identical to that in complex quantum mechanics.

An interesting feature of quantum corrections to the Bekenstein–Hawking entropy is the appearance of logarithmic area terms, whose coefficients are governed by the spectrum of massless fields. For near-extremal black holes, the entropy also receives a logarithmic temperature correction, whose coefficient is determined by the zero modes of the corresponding extremal black holes. In this paper, we study near-extremal rotating black holes in three, four, and five dimensions with an important focus on rotational zero modes. For three-dimensional BTZ black holes, our results are in agreement with the microscopic description. Furthermore, by treating the cosmological constant scale \(\ell\) as an independent parameter, we find an additional \(\log \ell\) correction to the entropy at extremality. For the five-dimensional BMPV black hole, we explicitly construct all the extremal zero modes and use them to evaluate the log temperature corrections to the entropy.

The Dirac quantum walk (a 1+1 dimensional space-time discretization of the Dirac equation) has a $2\mu$ mass gap both at the center and at the corner of the quasi-energy-momentum Brillouin zone. Gupta and Short recently noted [Quantum 9, 1845 (2025)] that the Dirac vacuum can create a particle-hole pair at the zone corner with the release of an energy $2\mu$ to the environment. They removed this vacuum instability at the expense of fermion doubling, the appearance of a second low-energy Dirac cone. Here we show that an alternative discretization scheme, with a tangent rather than a sine dispersion relation, offers stability while retaining a single Dirac cone. The key step is the Cayley transformation from the unit circle of Floquet eigenvalues $e^{-i\varepsilon}$ to the real line of unbounded energies $E=2\tan(\varepsilon/2)$. We compute the Schwinger effect (particle-hole pair creation in a uniform electric field) for tangent fermions and show that the pair-production rate agrees with the continuum result for a single Dirac cone. The zone corner is exactly decoupled if the scalar potential is coupled through the Hermitian generator of the quantum map. If it is coupled as a split operator, in order to preserve exact gauge invariance on the lattice, the corner does contribute - with a weight that vanishes quadratically with the lattice constants, in contrast to the Dirac quantum walk where the zone-corner instability survives the continuum limit.

We explore the construction of higher-dimensional Einstein-Maxwell(-Chern-Simons) solutions from vacuum seeds by means of a generalized Kerr-Schild transformation along a geodesic null vector field $\mathbf{k}$. Assuming the vector potential $\mathbf{A}$ to be aligned with $\mathbf{k}$, and $\mathbf{k}$ to be a Weyl aligned null direction satisfying the “optical constraint”, we arrive at three distinct branches of solutions. If $\mathbf{k}$ is expanding and twisting, then its shear must vanish – this branch includes certain charged Taub-NUT metrics. If $\mathbf{k}$ is expanding and twistfree, one finds two subfamilies: Robinson-Trautman electrovac solutions with a non-null Maxwell field if the shear is zero, or shearing solutions with a null field. Finally, the case when $\mathbf{k}$ is non-expanding reduces to a subset of the known Kundt solutions. In all cases, the Chern-Simons term turns out to be identically zero on-shell. In passing, by relaxing the alignment assumption on $\mathbf{A}$, we also obtain a six-dimensional extension of a charged Taub-NUT metric for which the magnetic part of the field strength is a linear combination of two distinct Kähler 2-forms, as opposed to the previously known examples in more than four dimensions.

Lipshitz and Sarkar asked in an ICM 2018 question whether their homotopy-theoretic refinement of Khovanov homology can detect mirror reflection when ordinary integral Khovanov homology cannot. We give an affirmative answer by presenting a prime knot whose integral Khovanov homology agrees with that of its mirror in every bidegree, including torsion, and yet over $\mathbb{F}_2$, the second Steenrod square has rank one for the knot and rank zero for its mirror in a specified bidegree. We also give a composite example. The construction, search and computations are done with the help of chat-GTP 5.6 sol Pro combing over the Regina Census of knots.

Pole-skipping occurs at special complex frequencies and momenta where the retarded Green function of a black-hole or black-brane background is not uniquely defined. The local near-horizon mechanism is well known: at resonance, a Frobenius recurrence matrix loses rank and the space of smooth horizon solutions enlarges. We address the global question of how two boundary-normalized solutions enter this resonant horizon solution space. For a general second-order scalar radial equation on a nonextremal background analytic near the horizon, the Frobenius recurrence at the resonant order yields a solvability condition. We prove that its vanishing is equivalent to singularity of the horizon recurrence matrix, absence of the logarithmic Frobenius term, and existence of two independent smooth horizon solutions. Away from resonance, the source zero is equivalent to horizon smoothness of the response-normalized solution, while the response zero is equivalent to horizon smoothness of the source-normalized solution. We then analyze the parameter-dependent simple pole of the nonresonant ingoing solution as resonance is approached. After removing this singularity, its resonant limit is proportional to the larger-root Frobenius solution, with proportionality factor given by the same solvability function. Continuing to the boundary shows that the same condition is equivalent to simultaneous vanishing of the two regularized boundary connection coefficients. This establishes a horizon-to-boundary dictionary between local Fuchsian resonance and the boundary source-response 0/0 structure of pole-skipping. Finally, different directions of approach can select different resonant solutions, with the selection governed by the first parameter variation of the same solvability function.

The magnetic Reissner-Nordstrom black hole embedded into the Bertotti-Robinson magnetic field is presented. Then it is used, as a seed, to generate, through the Harrison transformation of the Ersnt's equations, the Reissner-Nordstrom metric in the Bertotti-Robinson-Bonnor-Melvin magnetic field. Special cases generalising, the vacuum hairy type I Schwarzschild solution is discussed. The local equivalence between various forms of the Schwarzschild-Bertotti-Robinson is shown by exhibiting the explicit diffeomorphism.

One of the main advantages of the Loop-Tree Duality representation of scattering amplitudes is that it makes the origin of infrared and threshold singularities particularly transparent. This talk reviews recent progress in describing how singularities emerge and cancel at the level of scattering and vacuum amplitudes, discusses a novel strategy to efficiently construct finite integrals, and presents a complementary perspective based on encoding the underlying causal and singular structure in terms of qubits and quantum circuits.

We construct the electric and magnetic Carroll limits of the $\mathcal{O}(F^2)$-truncated $\text{D}_p$-brane via the Polyakov–KK route, which combines a single-mode Kaluza–Klein-like reduction at fixed light-cone momentum with a Dirac classification that keeps the auxiliary worldvolume frame. Unlike the $U(1)$-free ILST string, for $p\geq2$ the Carrollian D$_{p}$-brane cannot be treated as a consistent fixed-frame constrained system after the Dirac classification. In the electric family the obstruction is directly produced by the worldvolume $U(1)$ matter sector, while in the magnetic family the frame retention is forced by the scalar kinetic's density-weight structure rather than by the $U(1)$ currents. The frame must therefore be retained through the classification and eliminated afterwards by Dirac brackets. Freezing it beforehand is not a legitimate step in the Dirac procedure. The embedding scalar sector inherits the Carroll–Weyl $\chi$ structure at the level of the ILST kinetic density, which is $\chi$-invariant, whereas the full scalar action is only $\chi$-covariant. The local extension of $\chi$ to the full matter sector is obstructed by the $U(1)$ sector through the Gauss, circle and $A_-$-gradient brackets. The electric family keeps the global rescaling as a weak symmetry, while the magnetic family fails even for a global parameter. For $P_{-}\neq0$ the electric and magnetic families have $d-2$ and $d-3$ degrees of freedom, and the restored local circle at $P_{-}=0$ removes one further degree of freedom in each family. These features identify the resulting theories as constrained systems distinct from both the null string and the parent $\mathcal{O}(F^2)$ DBI theory, and we also discuss their on-shell interpretation and relation to tensionless/null strings.

We prove the shuffle realization for quantum affine superalgebras of types $B,C,D$ in the loop realization, in that we construct an isomorphism between each of these algebras and a suitably defined double shuffle algebra. We explicitly describe the latter shuffle algebra using certain vanishing conditions that generalize the Feigin-Odesskii wheel conditions; a novel feature is the appearance of a so-called scary wheel, which is a particular order $2$ vanishing condition involving $7$ variables. Along the way, we fully develop the theory of shrubs in super types $A$ (affine and toroidal), which are important combinatorial tools in the study of the shuffle algebras associated to toric Calabi-Yau threefolds. Our techniques also allow us to define quantum toroidal superalgebras of types $B,C,D$. More importantly, we provide a general framework to formulate and prove shuffle realizations in the wide generality of quivers with parameters.

We derive the background equations and complete odd- and even-parity quadratic actions for static, spherically symmetric black holes with radial scalar hair in general quartic-quintic Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, including Horndeski. On regular, nondegenerate branches, the formulation applies across Killing horizons and yields local no-ghost conditions and radial and angular eikonal characteristics. Tensor modes in both parity sectors share the same squared radial speed. When the radial coordinate is timelike, generic antisymmetric mixing induces nonstandard large-multipole scaling for both even-parity angular branches. Requiring both branches to have finite, nonzero eikonal phase speeds selects the Horndeski-related compatibility condition between the quartic and quintic beyond-Horndeski functions. This condition aligns the covariant degeneracy directions and permits a local disformal map to Horndeski when regular and invertible. For a finite, nonzero scalar kinetic term at the horizon, every nontrivial branch of the exact quadratic GLPV black hole is locally unstable or has a degenerate tensor cone near a simple outer horizon. Apart from identified exceptions, this obstruction extends to general shift- and reflection-symmetric quadratic GLPV theories and the regular Horndeski-related branch of the quartic-quintic class. Finally, for scalar-Gauss-Bonnet black holes with a vanishing horizon scalar kinetic term, we construct analytic power-law quartic beyond-Horndeski deformations whose associated quintic function is fixed by the same condition. At sufficiently small coupling, all local no-ghost and high-frequency gradient-stability conditions hold throughout the exterior. For a linear Gauss-Bonnet coupling, we estimate an interior scale below which the background and stability expansions lose perturbative control; this does not imply a physical instability.

We develop a comprehensive Floquet scattering theory for quantum transport in periodically driven nodal-ring semimetals (NRSs) and multi-Weyl semimetals (mWSMs), extending our earlier study reported in Annalen der Physik 535, 2200460 (2023), in which evanescent modes were neglected, to a complete formalism that includes both propagating and evanescent channels. By solving the full boundary-value problem, we obtain the complete set of scattering states and show that, although evanescent modes are indispensable for satisfying the matching conditions at the potential interfaces, they carry zero net probability current and do not contribute to any observable transport quantity. We identify a previously unexplored transport regime in NRSs in which two propagating channels coexist and participate in coherent scattering, producing multi-channel quantum interference and Floquet-induced Fano resonances. The transmission, reflection, pumped shot noise, and the associated Fano resonance features are determined entirely by the propagating channels, and the resonance energies coincide with those of the corresponding quasi-bound states of the static potential well. Our results establish a unified framework for Floquet transport in anisotropic topological semimetals, and confirm that the approximation of neglecting evanescent modes in our earlier work is justified for all measurable transport properties.

The strong $CP$ problem remains one of the major open questions in the Standard Model of particle physics. Its best-known solution is the Peccei–Quinn mechanism, which predicts a new pseudoscalar boson, the QCD axion. In recent years, alternative solutions and new perspectives on the foundations of the strong $CP$ problem have also received renewed attention. In this review, we provide a pedagogical account of the underlying physics and summarise the current theoretical and phenomenological status of the problem.

Numerical evidence has shown that a period of vanishing entropy production during far-from-equilibrium stages induces subsequent violations of the dominant energy condition in strongly coupled plasmas. This behavior also appears to hold for a Bjorken-expanding, hot and dense strongly coupled quantum fluid. In this context, it has been established that the chemical potential-to-temperature ratio ($\mu/T$) in the medium increases with higher initial charge density, $\rho_0$, and/or lower initial energy density, $\varepsilon_0$. Here, we present a numerical method to evolve Bjorken R-charged plasmas by varying $(\varepsilon_0,\rho_0)$ in order to generate a curve that preserves a constant $\mu/T$. This allows us to address the case in which all Bekenstein-Hawking entropy densities evolve towards configurations with the same $\mu/T$. This approach enables a more direct comparison with the $\mathcal{N}=4$ SYM plasma case ($\mu/T=0$) and, consequently, provides clearer evidence of the correlation between entropy production and violations of the dominant energy condition. Moreover, this procedure offers a characterization (albeit numerical and partial) of the iso$-\mu/T$ entropy density hydrodynamic attractor for hot and dense strongly coupled quantum fluids.

Recently in the physics literature there have been a small, but growing, number of papers that have applied the Eynard-Orantin topological recursion procedure to spectral curves with ramification loci of infinite cardinality. However, there is a corresponding gap in the mathematics literature; indeed, it has not been checked rigorously whether the resulting infinite sums converge, or whether the resulting correlators have all the desired properties of the topological recursion. The present work aims to bridge this gap by defining topological recursion on a suitably broad class of spectral curves to cover the aforementioned physics applications and to rigorously prove that this definition has the properties one would intuitively expect. As a by-product, some interesting coincidences involving quantum curves are discovered, where two different spectral curves yield the same quantum curve, a situation that has, hitherto, not appeared in the literature.

The gravitational energies of timelike singularities in some asymptotically AdS spaces and in the Schwarzschild black hole with negative mass are explicitly computed. In all cases considered, the energy is finite and positive, depends on the geometry around the singularity, and compensates negative energy contributions from the asymptotic boundary, rendering the total gravitational energy positive. The definition used for energy is the on-shell Hamiltonian of the physical classical action proposed by Hawking and Horowitz~\cite{Hawking-Horowitz}. To deal with the singularity, spacetime is cut off by a timelike regulating boundary surrounding the singularity that is compatible with a foliation of spacetime in constant-time slices. It is shown that the total energy of static AdS-Kasner solutions with timelike Kasner singularities is equal to the energy of the planar AdS black hole, and that the Schwarzschild black hole with negative mass has the same energy as Minkowski space.

Motivated by deformations of spin structures and their geometric implications, we study a deformed exterior derivative, which is a third-order nilpotent operator. This higher-order differential structure induces an anholonomic rescaling of the local frame and leads to a bifurcation of the associated cohomological structure, with two distinct notions of closedness and exactness. We prove that the Poincaré Lemma fails in both sectors, so that closed deformed forms need not be exact even locally. We then apply the resulting framework to a four-dimensional effective field theory and show that a constant saturation of the deformation parameter can generate a hierarchy between the electroweak and fundamental Planck scales through a purely geometric mechanism, without introducing extra spatial dimensions.

Let $G$ be a complex reductive affine algebraic group with its symmetric tensor category $\mathcal{C}_G$ of finite-dimensional rational representations. We prove that every simple commutative algebra object with at most countable dimension in the direct limit completion $\operatorname{Ind}(\mathcal{C}_G)$ of $\mathcal{C}_G$ is isomorphic to the algebra $\mathcal{O}(G/H)$ of regular functions on the homogeneous space $G/H$, for some reductive algebraic subgroup $H$ of $G$. Then we apply this result to the theory of vertex operator algebra extensions. In particular, assuming the strong rationality of the $ \operatorname{A}_5$-orbifold of the vertex operator algebra $V_{\mathcal{L}_2}$ associated with the rank-one root lattice $\mathcal{L}_2:= \sqrt{2}\mathbb{Z}$, we classify all the not necessarily rational simple CFT type preunitary vertex operator algebra extensions of the simple unitary Virasoro vertex operator algebra $L(1,0)$ with central charge $c=1$ satisfying a certain spectrum condition. This result is the vertex operator algebra analogue of a conformal net result by Feng Xu. Every strongly rational preunitary vertex operator algebra extension of $L(1,0)$ satisfies the above spectrum condition because of the congruence subgroup modularity property of its characters. As a consequence, we get a complete classification result for strongly rational $c=1$ vertex operator algebras, up to the strong rationality of $V_{\mathcal{L}_2}^{\operatorname{A}_5}$.

A three-matrix model that contains a plethora of fuzzy sphere solutions was defined twenty years ago. It has been shown that in a certain regime of the model, combinations of fuzzy spheres become classical solutions of the model. In the original paper and subsequent works, the stability of specific states has been discussed, showing that only a single largest fuzzy-sphere configuration is stable. Here, we focus on a complementary question: starting from some initial configuration, is the thermodynamically preferred state approached rapidly, or are there other long-lived, metastable configurations which may support interesting physics? We find that the answer in the large-matrix limit depends on the dispersion of the initial configuration. We identify the elementary transition as an accretion, in which one sphere absorbs a single unit from another, and show that it is driven by fluctuations of the sphere centers. By measuring these fluctuations in long simulations, we find quantitative agreement with the one-loop effective action, with no free parameters. For multi-sphere states, we find that the stiffness of an inner sphere grows logarithmically with the number of surrounding layers, so that concentric onion-like configurations – describing an emergent three-dimensional quantum space – become increasingly long-lived.

We consider the effects of radiative corrections in Starobinsky-like models of inflation, concentrating on models of inflation formulated in N=1 no-scale supergravity. Inflaton couplings to matter fields are necessary for reheating and these have an impact on loop corrections to the inflaton potential. Whilst corrections due to the supergravity couplings of the inflaton to Standard Model (MSSM) fields are negligible, we use Planck data to obtain interesting constraints on GUT bilinear couplings, vevs, and gauge boson masses that could be sharpened by future CMB measurements.

The boundary of a $3{+}1$-dimensional topological superconductor carries a $\mathbb{Z}_{16}$-valued global (Dai-Freed) anomaly, famously matched by the $16$ fermions of a Standard Model generation once a certain $\mathbb{Z}_4$ symmetry is gauged. In a supergravity completion, though, a gravitino contributes $-7/16$ rather than $\pm1/16$, obstructing this $\mathbb{Z}_4$ in the Minimal Supersymmetric Standard Model. We observe that four-dimensional $\mathcal{N}=8$ supergravity evades this fate. Its fermions, eight gravitini in the $\mathbf 8$ and fifty-six spin-$\tfrac12$ states in the $\mathbf{56}=\Lambda^3\mathbf 8$ of the $SU(8)$ R-symmetry, cancel the anomaly. The cancellation holds for every admissible $\mathbb{Z}_4$ structure, is consistent with the vanishing of the continuous $SU(8)$ anomaly, and follows from a Smith homomorphism and the Rarita-Schwinger ghost-subtraction weight identifying the supergravity anomaly with that of the topological superconductor. In maximal supergravity this $\mathbb{Z}_4$ stays anomaly-free and gaugeable despite its eight gravitini. All numbers are reproduced by an open-source library described in the Supplemental Material.