UV-divergences of Wilson Loops for Gauge/Gravity Duality

TL;DR

This paper investigates the UV divergence structure of Wilson loops in gauge/gravity duality, revealing new divergences caused by B-fields and metrics, and analyzing conditions for their cancellation in various supergravity backgrounds.

Contribution

It identifies new UV divergences in Wilson loops due to B-fields and metrics, and derives conditions under which these divergences can be canceled, extending previous analyses involving dilatons.

Findings

Legendre transform cannot cancel divergences from B-fields in general.

Many supergravity backgrounds, including Sakai-Sugimoto and Sasaki-Einstein spaces, satisfy conditions for divergence cancellation.

Wilson loops in Klebanov-Strassler background have non-cancellable B-field divergences.

Abstract

We analyze the structure of the UV divergences of the Wilson loop for a general gauge/gravity duality. We find that, due to the presence of a nontrivial NSNS B-field and metric, new divergences that cannot be subtracted out by the conventional Legendre transform may arise. We also derive conditions on the B-field and the metric, which when satisfied, the leading UV divergence will become linear, and can be cancelled out by choosing the boundary condition of the string appropriately. Our results, together with the recent result of arXiv:0807.5127, where the effect of a nontrivial dilaton on the structure of UV divergences in Wilson loop is analysed, allow us to conclude that Legendre transform is at best capable of cancelling the linear UV divergences arising from the area of the worldsheet, but is incapable to handle the divergences associated with the dilaton or the B-field in general. We also solve the conditions for the cancellation of the leading linear divergences generally and find that many well-known supergravity backgrounds are of these kinds, including examples such as the Sakai-Sugimoto QCD model or N=1 duality with Sasaki-Einstein spaces. We also point out that Wilson loop in the Klebanov-Strassler background have a divergence associated with the B-field which cannot be cancelled away with the Legendre transform. Finally we end with some comments on the form of the Wilson loop operator in the ABJM superconformal Chern-Simons theory.