Conformal Field Theory and Algebraic Structure of Gauge Theory

TL;DR

This paper explores the algebraic structures underlying gauge theories and conformal field theories, focusing on homotopy algebras like Yang-Mills $L_{ infty}$ and $C_{ infty}$, and their connections to Lian-Zuckerman type structures.

Contribution

It establishes new links between homotopy algebras in gauge theories and algebraic structures in conformal field theory, including examples with matter fields.

Findings

Identified relations between Yang-Mills $L_{ infty}$ and $C_{ infty}$ algebras and CFT structures.

Provided examples of gauge theory algebras involving matter fields.

Analyzed algebraic structures in first order formulations of gauge theories.

Abstract

We consider various homotopy algebras related to Yang-Mills theory and two-dimensional conformal field theory (CFT). Our main objects of study are Yang-Mills $L_{\infty}$ and $C_{\infty}$ algebras and their relation to the certain algebraic structures of Lian-Zuckerman type in CFT. We also consider several examples of algebras related to gauge theory, involving first order formulations and gauge theories with matter fields.