A Worldsheet Description of Planar Yang-Mills Theory

TL;DR

This paper develops a worldsheet framework for planar Yang-Mills theory, incorporating Grassmann variables, which naturally reproduces all interaction vertices including quartic ones, advancing the string-theoretic understanding of gauge theories.

Contribution

It introduces a worldsheet description of non-abelian gauge theory with Grassmann variables, enabling automatic derivation of all interaction vertices.

Findings

Successfully reproduces all gluon interaction vertices from the worldsheet formalism.

Extends previous work by incorporating Grassmann variables similar to string theory.

Provides a new perspective on gauge theories through a string-inspired worldsheet approach.

Abstract

We extend previous work by developing a worldsheet description of non-abelian gauge theory (Yang-Mills). This task requires the introduction of Grassmann variables on the world sheet analogous to those of the Neveu-Schwarz-Ramond formulation of string theory. A highlight of our construction is that once the three gluon vertices of Yang-Mills Feynman diagrams are given a worldsheet description, the worldsheet formalism automatically produces all of the quartic vertices.