相关论文: Vertex algebras, topological defects, and Moonshin…

Let $W$ be an irreducible complex reflection group acting on its reflection representation $V$. We consider the doubly graded action of $W$ on the exterior algebra $\wedge (V \oplus V^*)$ as well as its quotient $DR_W := \wedge (V \oplus…

This contribution is mainly based on joint papers with Lepowsky and Milas, and some parts of these papers are reproduced here. These papers further extended works by Lepowsky and by Milas. Following our joint papers, I explain the general…

The topological theory and the Volterra process are key tools for the classification of defects in Condensed Mater Physics. We employ the same methods to classify the 2D defects of a 4D maximally symmetric spacetime. These \textit{cosmic…

We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…

Vertex algebras (and their modules) can be described as vector spaces together with a linear operator-valued series in one parameter $z$. With the interpretation of $z$ as a coordinate at a point on a curve, one can construct algebraic…

Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences. They are energetically costly (the energy…

We precisely determined an $\bN$-graded structure of Zhu's poisson algebra $V/C_2(V)$ of vertex operator algebras $V$ of moonshine type. Namely, if $V$ is a vertex operator algebra of moonshine type with a central charge $24$, then…

For vector lattices $E$ and $F$, where $F$ is Dedekind complete and supplied with a locally solid topology, we introduce the corresponding locally solid absolute strong operator topology on the order bounded operators $\mathcal…

We describe a relationship between the representation theory of the Thompson sporadic group and a weakly holomorphic modular form of weight one-half that appears in work of Borcherds and Zagier on Borcherds products and traces of singular…

It is typical for a semi-infinite cohomology complex associated with a graded Lie algebra to occur as a vertex operator (or chiral) superalgebra where all the standard operators of cohomology theory, in particular the differential, are…

We extend formulae which measure discrepancies for regularized traces on classical pseudodifferential operators to regularized trace cochains, regularized traces corresponding to 0-regularized trace cochains. This extension from 0-cochains…

In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large $r$, the $r$\textsuperscript{th} Veronese subalgebra of a Cohen-Macaulay standard graded $K$-algebra has properties similar…

It has been known since 1992 that the McKay-Thompson series $T_g(q)$ of the Moonshine module form Hauptmoduln for genus zero subgroups of $SL(2, \mathbb{R})$. In 2021, Lin and Shao constructed a series analogous to the McKay-Thompson series…

We introduce a notion of Hecke-monicity for functions on certain moduli spaces associated to torsors of finite groups over elliptic curves, and show that it implies strong invariance properties under linear fractional transformations.…

In this paper we investigate the relation between complexified Fenchel-Nielsen coordinates and spectral network coordinates on Seiberg-Witten moduli space. The main technique is the comparison of exact expressions for the expectation value…

A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to…

We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Mili\v{c}i\'c-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra…

We study topological defect lines in the symmetric-product orbifolds $\mathrm{Sym}^N(X)$ for a generic seed CFT $X$. We focus on the defects which preserve the maximum of the $S_N$ symmetry. When $X$ is taken to describe the free theory of…

Given a finite group $\Gamma$ and a virtual character $\wt$ on it, we construct a Fock space and associated vertex operators in terms of representation ring of wreath products $\Gamma\sim S_n$. We recover the character tables of wreath…

We prove that all holomorphic vertex operator algebras of central charge $24$ with non-trivial weight one subspaces are unitary. The main method is to use the orbifold construction of a holomorphic VOA $V$ of central charge $24$ directly…