Zeta-function Regularization of Holographic Wilson Loops

TL;DR

This paper applies zeta-function regularization to compute the one-loop effective action of strings in AdS5×S5, comparing holographic Wilson loops with field theory results, and finds partial agreement with some discrepancies at higher orders.

Contribution

It introduces a zeta-function regularization approach to evaluate holographic Wilson loops and addresses ambiguities by subtracting the half-BPS case, providing new insights into string theory calculations.

Findings

Agreement with field theory at first order in small latitude expansion

Discrepancies observed at higher order in the expansion

Method clarifies regularization issues in holographic Wilson loop computations

Abstract

Using $\zeta$-function regularization, we study the one-loop effective action of fundamental strings in $AdS_5\times S^5$ dual to the latitude $\frac{1}{4}$-BPS Wilson loop in $\mathcal{N}=4$ Super-Yang-Mills theory. To avoid certain ambiguities inherent to string theory on curved backgrounds we subtract the effective action of the holographic $\frac{1}{2}$-BPS Wilson loop. We find agreement with the expected field theory result at first order in the small latitude angle expansion but discrepancies at higher order.