Non-commutative Gauge Theory, Open Wilson Lines and Closed Strings

TL;DR

This paper explores the link between non-commutative gauge theories and closed strings via open Wilson lines, highlighting reparametrization invariance and gauge symmetries that mirror closed string properties.

Contribution

It proposes that reparametrization invariance determines the coupling of non-commutative gauge theories to closed string modes and identifies conserved operators analogous to string symmetries.

Findings

Reparametrization invariance governs Wilson line coupling to closed strings.

The generating functional exhibits expected closed string gauge symmetry.

An infinite set of conserved operators, including the stress tensor, is identified.

Abstract

A recently proposed connection between closed string field and an open Wilson line defined on an arbitrary contour is further explored here. We suggest that reparametrization invariance of a Wilson line is the principle which determines the coupling of non-commutative gauge theory/matrix model to the modes of the closed string. An analogue of the level matching condition on the gauge theory/matrix model operators emerges quite naturally from the cyclic symmetry of the straight Wilson line. We show that the generating functional of correlation functions of these operators has the space-time gauge symmetry that one expects to find in closed string field theory. We also identify an infinite number of conserved operators in gauge theory/matrix model, the first of which is known to be the conserved stress tensor.