Duality and Non-Commutative Gauge Theory

TL;DR

This paper explores the extension of S-duality to non-commutative gauge theories, revealing how duality transforms the nature of non-commutativity and implications for locality in time.

Contribution

It provides a leading-order analysis of dual non-commutative gauge theories via Legendre transformation, highlighting the duality's effects on non-commutativity and coupling.

Findings

Dual theories are weakly coupled when original theories are strongly coupled under proper scaling.

Dual descriptions can become non-commutative in space-time even if original theories are space-space non-commutative.

Locality in time may be an artifact of perturbation theory in non-commutative gauge theories.

Abstract

We study the generalization of S-duality to non-commutative gauge theories. For rank one theories, we obtain the leading terms of the dual theory by Legendre transforming the Lagrangian of the non-commutative theory expressed in terms of a commutative gauge field. The dual description is weakly coupled when the original theory is strongly coupled if we appropriately scale the non-commutativity parameter. However, the dual theory appears to be non-commutative in space-time when the original theory is non-commutative in space. This suggests that locality in time for non-commutative theories is an artifact of perturbation theory.