The Partition Function of a Wilson Loop in a Strongly Coupled $\mathcal N=4$ Supersymmetric Yang-Mills Plasma with Fluctuations

TL;DR

This paper calculates the one-loop partition function of superstring fluctuations in a Schwarzschild-AdS$_5\times S^5$ background, confirming divergence cancellations and comparing different string actions for Wilson loops.

Contribution

It provides a detailed derivation of the superstring partition function in a thermal AdS background, including equivalence of string actions and divergence cancellation.

Findings

Partition functions for Wilson lines are derived.

UV divergences are shown to cancel.

Equivalence of Nambu-Goto and Polyakov actions is demonstrated.

Abstract

We examine the one-loop partition function describing the fluctuations of the superstring in a Schwarzschild-AdS$_5\times S^5$ background. On the bosonic side, we demonstrate the one-loop equivalence of the Nambu-Goto action and the Polyakov action for a general worldsheet, while on the fermionic side, we consider the reduction of the ten-dimensional Green-Schwarz fermion action to a two-dimensional worldsheet action. We derive the partition functions of the worldsheets corresponding to both straight and parallel Wilson lines. We show that the UV divergences of the functional determinants in the thermal AdS background are canceled.