Toward precision holography with supersymmetric Wilson loops

TL;DR

This paper tests the AdS/CFT correspondence for supersymmetric Wilson loops by comparing quantum string fluctuation calculations with gauge theory predictions, revealing a discrepancy at next-to-leading order.

Contribution

It provides a detailed quantum fluctuation analysis of 1/4 BPS Wilson loops in AdS/CFT, highlighting sources of mismatch with gauge theory results.

Findings

Discrepancy found between string theory and gauge theory at one-loop level.

Identified specific fluctuation modes responsible for the mismatch.

Compared 1/4 BPS and 1/2 BPS configurations to analyze zero mode ambiguities.

Abstract

We consider certain 1/4 BPS Wilson loop operators in SU(N) ${\cal N}=4$ supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS5 x S5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.