OPE between the energy-momentum tensor and the Wilson loop in N=4 Super-Yang-Mills theory

TL;DR

This paper investigates the operator product expansion between the energy-momentum tensor and Wilson loops in N=4 Super-Yang-Mills theory, showing that Wilson loops are invariant under conformal transformations aside from shape changes.

Contribution

It clarifies that Wilson loops in N=4 SYM do not have anomalous dimensions and are only affected by conformal transformations through shape modifications.

Findings

Wilson loops have no anomalous dimension in N=4 SYM.

Conformal transformations alter Wilson loop shape, not their scaling dimensions.

The OPE between the energy-momentum tensor and Wilson loops is explicitly analyzed.

Abstract

We analyze the operator product expansion T_{\mu \nu}(z) W[C] in N=4 4-dimensional Super-Yang-Mills (SYM) theory with U(N) gauge group, and clarify that the closed Wilson loop does not possess an anomalous dimension and that only the shape of the loop is changed by the conformal transformation.