Related papers: Chiral Algebra, Localization, Modularity, Surface …
In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are…
In this paper we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu algebras and bimodules (and their $g$-twisted analogs) are Noetherian. These carry important information about the…
We study three families of infinite-dimensional Lie algebras defined from Vertex Operator Algebras and their properties. For $N=0$ VOAs, we review the construction of the Fock space $V_L$ from an even lattice $L$ and provide an algebraic…
The usual spinor construction from one fermion yields four irreducible representations of the Virasoro algebra with central charge $c = 1/2$. The Neveu-Schwarz (NS) sector is the direct sum of an $h = 0$ and an $h = 1/2$ module, and the…
The Schur limit of the superconformal index of four-dimensional $\mathcal N=2$ superconformal field theories has been shown to equal the supercharacter of the vacuum module of their associated chiral algebra. Applying localization…
There is a special set of massless four-dimensional gauge theories which admit local and gauge-anomaly-free uplifts to twistor space; we call such theories twistorial. In twistorial theories, generalized towers of soft modes (including…
Conformal field theory and its axiomatisation in terms of vertex operator algebras or chiral algebras are most commonly considered on the Riemann sphere. However, an important constraint in physics and an interesting source of mathematics…
It is one of the remarkable results of vertex operator algebras (VOAs) that the graded traces (one-point correlation functions) of holomorphic VOAs are modular functions. This paper explores the question of which modular functions arise as…
The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite group and its…
We consider 4d $\mathcal{N}=1$ gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry…
We introduce a family of dualities between certain non-supersymmetric self-dual gauge theories on a large class of $4d$ self-dual asymptotically flat backgrounds, and the large $N$ limit of an independently defined $2d$ chiral defect CFT.…
In this paper, we prove that simple affine vertex operator algebras with positive integral levels admit only trivial first-order deformations. Therefore, the deformation rigidity conjecture of strongly rational vertex operator algebras…
The representation theory of affine Kac-Moody Lie algebras has grown tremendously since their independent introduction by Robert V. Moody and Victor G. Kac in 1968. Inspired by mathematical structures found by theoretical physicists, and by…
Let $\mathbb V$ be an $\mathbb N$-graded, $C_2$-cofinite vertex operator algebra (VOA) admitting a non-lowest generated module in $\mathrm{Mod}(\mathbb V)$ (e.g., the triplet algebras $\mathcal{W}_p$ for $p\in \mathbb{Z}_{\geq 2}$ or the…
We find an intriguing relation between the chiral algebra and the mixed Hodge structure of the Coulomb branch of four dimensional $\mathcal{N} = 2$ superconformal field theories. We identify the space of irreducible characters of the…
This paper is a review of open-closed rational conformal field theory (CFT) via the theory of vertex operator algebras (VOAs), together with a proposal of a new geometry based on CFTs and D-branes. We will start with an outline of the idea…
We investigate superconformal surface defects in four-dimensional N=2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module.…
We study a differential graded VOA associated to the derived critical locus of a function $f$ on a smooth oriented $D$-dimensional variety $(X,\mathbf{vol})$. Informally, this VOA, $\mathbf{crit}^{ch}_{f}$, is just the algebra of chiral…
We provide a general formula for the partition function of three-dimensional $\mathcal{N}=2$ gauge theories placed on $S^2 \times S^1$ with a topological twist along $S^2$, which can be interpreted as an index for chiral states of the…
We show that the representation theory for the toroidal extended affine Lie algebras is controlled by a vertex operator algebra which is a tensor product of four VOAs: a sub-VOA of the hyperbolic lattice VOA, two affine VOAs and a Virasoro…