Related papers: Non-Connected Gauge Groups and the Plethystic Prog…
Inspired by the discovery of quantum hall effect and topological insulator, topological properties of classical waves start to draw worldwide attention. Topological non-trivial bands characterized by non-zero Chern numbers are realized with…
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries…
This is the first of two papers on the superselection sectors of the conformal model in the title, in a time zero formulation. A classification of the sectors of the net of observables as restrictions of solitonic (twisted) and…
A complexified Heisenberg matrix group $\mathrm{H}_\mathbb{C}$ with entries from an infinite-dimensional Hilbert space $H$ is investigated. The Weyl--Schr\"odinger type irreducible representations of $\mathrm{H}_\mathbb{C}$ on the space…
Boris Tsirelson constructed an uncountable family of type III product systems of Hilbert spaces through the theory of Gausian spaces, measure type spaces and `slightly coloured noises', using techniques from probability theory. Here we take…
Supersymmetric gauge theories of certain class possess a large hidden nonperturbative symmetry described by the Ding-Iohara-Miki (DIM) algebra which can be used to compute their partition functions and correlators very efficiently. We lift…
We define and study a class of $\mathcal{N}=2$ vertex operator algebras $\mathcal{W}_{\mathcal{\mathsf{G}}}$ labelled by complex reflection groups. They are extensions of the $\mathcal{N}=2$ super Virasoro algebra obtained by introducing…
This article delves into the analysis of various spectral properties pertaining to totally paranormal closed operators, extending beyond the confines of boundedness and encompassing operators defined in a Hilbert space. Within this class,…
Let (g,[p]) be a finite-dimensional restricted Lie algebra, defined over an algebraically closed field k of characteristic p>0. The scheme of tori of maximal dimension of g gives rise to a finite group S(g) that coincides with the Weyl…
We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in…
Coulomb branches of a set of $3d\ \mathcal{N}=4$ supersymmetric gauge theories are closures of nilpotent orbits of the algebra $\mathfrak{so}(n)$. From the point of view of string theory, these quantum field theories can be understood as…
We study representation zeta functions of finitely generated, torsion-free nilpotent groups which are rational points of unipotent group schemes over rings of integers of number fields. Using the Kirillov orbit method and p-adic…
We construct a Weyl x SU(2)_L x U(1)_Y invariant theory by extending four-dimensional Weyl quadratic gravity with Weyl-invariant scalar, fermion, Yukawa and gauge sectors. The quadratic structure (R^tilde - mu^2 |phi|^2)^2 allows the Weyl…
We suggest a programming realization of an algorithm for verifying a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan…
Starting from Maxwell-Weyl algebra we found the transformation rules for generalized space-time coordinates and the differential realization of corresponding generators. By treating local gauge invariance of Maxwell-Weyl group, we presented…
We study non-elliptic quadratic differential operators. Quadratic differential operators are non-selfadjoint operators defined in the Weyl quantization by complex-valued quadratic symbols. When the real part of their Weyl symbols is a…
A procedure to determine the initial ansatz for the co-frame and spin connection characterizing a Riemann-Cartan geometry respecting a given group of continuous symmetries is illustrated. Given a particular group of symmetries and assuming…
We study the quantum dynamics of a system of $n$ Abelian ${\cal N}=1$ vector multiplets coupled to $\frac 12 n(n+1)$ chiral multiplets which parametrise the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. In the…
I present several applications of the Dirac inequality to the determination of isolated unitary representations and associated "spectral gaps" in the case of unramified principal series. The method works particularly well in order to attach…
The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion…