Steps Towards Generalization of Tensionless String Theory with Contact Interactions as Wilson loop of Non-Abelian Yang-Mills Theory

TL;DR

This paper introduces a modified tensionless string model with contact interactions that aims to replicate non-Abelian Wilson loop expectations in Yang-Mills theory, utilizing Lie algebra-valued fields and topological BF action.

Contribution

It proposes a novel tensionless string framework incorporating contact interactions and Lie algebra fields to reproduce non-Abelian Wilson loops, advancing the understanding of gauge-string duality.

Findings

Model reproduces non-Abelian Wilson loop expectations

Discards effects of self-interactions in the Wilson loop

Tests with SU(2) show promising results for three-point interactions

Abstract

We propose a possible modification to the tensionless string model with contact interactions. The proposed model aims to reproduce an expectation value of the non-Abelian Wilson loop in the Yang-Mills theory when integrating out string degrees of freedom with a fixed worldsheet boundary. Lie algebra-valued fields whose dynamics are determined by the topological BF action are introduced on the string worldsheet to reproduce path-ordering along the worldsheet boundary. Without bulk contributions, we show that the model describes the non-Abelian Wilson loop discarding effects of self-interactions. Finally, a reproduction of the Wilson loop with three-point interaction is tested in the case of $SU(2)$