Wilson Line Correlators in N=4 Non-commutative Gauge Theory on S^2 x S^2

TL;DR

This paper studies Wilson line correlators in a non-commutative N=4 gauge theory on S^2 x S^2, revealing UV/IR mixing effects and proposing a renormalization method to define finite, local operators.

Contribution

It introduces a novel analysis of Wilson line correlators in non-commutative gauge theory, highlighting UV/IR mixing and a renormalization scheme for finite, local operators.

Findings

Identifies non-analytic contributions due to UV/IR mixing.

Proposes a renormalization procedure for operators without anomalous dimensions.

Shows supergravity accounts for IR and UV/IR effects.

Abstract

We investigate the Wilson line correlators dual to supergravity multiplets in N=4 non-commutative gauge theory on S^2 x S^2. We find additional non-analytic contributions to the correlators due to UV/IR mixing in comparison to ordinary gauge theory. Although they are no longer BPS off shell, their renormalization effects are finite as long as they carry finite momenta. We propose a renormalization procedure to obtain local operators with no anomalous dimensions in perturbation theory. We reflect on our results from dual supergravity point of view. We show that supergravity can account for both IR and UV/IR contributions.