$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular graphs, using permutation group techniques. We also list their generating functions and give (software) algorithms computing their number at an arbitrary rank and

In [13], a new quasi-local energy is introduced for spacetimes with a non-zero cosmological constant. In this article, we study the small sphere limit of this newly defined quasi-local energy for spacetimes with a negative cosmological constant. For such spacetimes, the anti de‑Sitter space is used as the reference for the quasi-local energy. Given a point $p$ in a spacetime $N$, we consider a canonical

In the usual approaches to mechanics (classical or quantum) the primary object of interest is the Hamiltonian, from which one tries to deduce the solutions of the equations of motion (Hamilton or Schrödinger). In the present work we reverse this paradigm and view the motions themselves as being the primary objects. This is made possible by studying arbitrary phase space motions, not of points, but

We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner–Nordström spacetime. The equations are derived in the context of global nonlinear stability of Reissner–Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on non-linear stability of Schwarzschild spacetime of Klainerman–Szeftel ([9]). The main

For a three dimensional nilmanifold together with a three form on it, we build a module $\mathcal{H}$ of an affine Kac–Moody vertex algebras. Then, we associate logarithmic fields to the module $\mathcal{H}$ and we study their singularities. We also present a physics motivation behind this construction. We study a particular case, we show that when the nilmanifold $N$ is a $k$ degree $S^1$-fibration

We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi–Yau manifolds are investigated in particular.

The path integral for the partition function of Chern–Simons gauge theory with a compact gauge group is evaluated on a general Seifert $3$-manifold. This extends previous results and relies on abelianisation, a background field method and local application of the Kawasaki Index theorem.

For any positive integer $n$ and any Lie group $\mathfrak{G}$, given a definite symmetric bilinear form on $\mathbb{R}^n$ and an Ad‑invariant scalar product on the Lie algebra of $\mathfrak{G}$, we construct a variational problem on fields defined on an arbitrary oriented $(n + \operatorname{dim} \mathfrak{G})$-dimensional manifold $\mathcal{Y}$. We show that, if $\mathfrak{G}$ is compact and simply

The 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kähler manifold $X$, which is reproduced in the IR limit. We propose and explore a 3d lift of this correspondence, where the UV model is the $\mathcal{N} = 2$ supersymmetric 3d gauge theory and the IR limit is given by Givental’s permutation equivariant quantum K‑theory on $X$. This gives a one-parameter deformation

We investigate F-theory models with a discrete $\mathbb{Z}_2$ gauge symmetry and $SU(n)$ gauge symmetries. We utilize a class of rational elliptic surfaces lacking a global section, known as Halphen surfaces of index $2$, to yield genus-one fibered K3 surfaces with a bisection, but lacking a global section. We consider F‑theory compactifications on these K3 surfaces times a K3 surface to build such

In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied within the recently developed Orlicz space based approach to large systems. This means that the proposed approach successfully provides a refined framework for the

We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one can develop several concepts in a close analogy with the latter. In particular, we exhibit a countable number of nontrivial projections in the algebra of the noncommutative

The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the push-forward under a diffeomorphism. Then the constructions are extended to convex combinations of such measures, leading to perturbation expansions for the mean and the fluctuation of

We establish a higher generalization of super $L_\infty$‑algebraic T‑duality of super WZW‑terms for super p-branes. In particular, we demonstrate spherical T‑duality of super M5‑branes propagating on exceptional-geometric 11d super spacetime.

We elucidate the correspondence between a particular class of superconformal field theories in six dimensions and homomorphisms from discrete subgroups of $SU(2)$ into $E_8$, as predicted from string dualities. We show how this match works for homomorphisms from the binary icosahedral group $SL(2, 5)$ into $E_8$, correcting previous errors in both the mathematics and physics literature. We use this

Motivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation in terms of the Maurer–Cartan equation associated to differential forms valued in $L_\infty$-algebras. The elimination of auxiliary variables of Vasiliev equation