Chiral Deformations of Conformal Field Theories

TL;DR

This paper investigates how holomorphic perturbations affect 2D conformal field theories, revealing algebraic structures that influence their partition functions and applications across various mathematical physics domains.

Contribution

It introduces a contact term algebra framework for understanding genus one partition functions under chiral deformations of CFTs.

Findings

Partition functions are governed by a contact term algebra derived from OPEs.

Applications to vertex operator algebras and 2D QCD are demonstrated.

Insights into modular properties and holomorphic anomalies of chiral algebras are provided.

Abstract

We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the $W_{1+\infty}$ algebra, that is treated in detail.