Two Dimensional Conformal Field Theory and a Primer to Chiral Algebras

TL;DR

This paper reviews the algebraic structures in two-dimensional conformal field theories, focusing on chiral algebras like the Virasoro algebra and their extensions with additional symmetries.

Contribution

It provides a compact overview of the emergence and role of chiral algebras in 2D conformal field theories, including extended symmetries.

Findings

Chiral algebras are central to the symmetry structure of 2D CFTs.

Extended chiral algebras arise naturally with additional symmetries.

The Virasoro algebra underpins local conformal symmetry in 2D CFTs.

Abstract

We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra related to local conformal symmetry, namely the Virasoro algebra. We then introduce two dimensional conformal field theories with additional symmetries in which extended chiral algebras emerge as a natural generalization of the conformal case.