Yang-Mills theory from the worldsheet

TL;DR

This paper introduces a novel worldsheet-based approach to classical Yang-Mills theory by coupling a chiral conformal field theory, revealing new insights into gauge anomalies and the theory's structure.

Contribution

It provides a new worldsheet formulation of Yang-Mills theory, connecting it to string theory concepts and analyzing anomaly conditions.

Findings

The model is solvable and reproduces Yang-Mills equations via anomaly cancellation.

Decoupling gravity yields classical Yang-Mills equations as anomaly conditions.

Reinstating gravitational modes introduces gauge anomalies similar to heterotic strings.

Abstract

We give a new description of classical Yang-Mills theory by coupling a two-dimensional chiral CFT (which gives the tree-level S-matrix of Yang-Mills theory at genus zero) to a background non-abelian gauge field. The resulting model is solvable, and when the gravitational degrees of freedom are decoupled the non-linear Yang-Mills equations are imposed as an exact worldsheet anomaly cancellation condition. When gravitational modes are reinstated, we find gauge anomalies analogous to those appearing in heterotic string theory.