Limiting Geometries of Two Circular Maldacena-Wilson Loop Operators

TL;DR

This paper analyzes two-loop calculations of circular Maldacena-Wilson loops in N=4 gauge theory, revealing their non-BPS nature due to unprotected operators and challenging a Gaussian matrix model conjecture.

Contribution

It adapts previous calculations to symmetric loops, explores local operator expansions, and provides a two-loop test questioning the Gaussian matrix model conjecture.

Findings

Circular Maldacena-Wilson loops are non-BPS due to unprotected operators.

Explicit two-loop calculations show anomalous dimensions from non-ladder diagrams.

The Gaussian matrix model conjecture is challenged by new two-loop evidence.

Abstract

We further analyze a recent perturbative two-loop calculation of the expectation value of two axi-symmetric circular Maldacena-Wilson loops in N=4 gauge theory. Firstly, it is demonstrated how to adapt the previous calculation of anti-symmetrically oriented circles to the symmetric case. By shrinking one of the circles to zero size we then explicitly work out the first few terms of the local operator expansion of the loop. Our calculations explicitly demonstrate that circular Maldacena-Wilson loops are non-BPS observables precisely due to the appearance of unprotected local operators. The latter receive anomalous scaling dimensions from non-ladder diagrams. Finally, we present new insights into a recent conjecture claiming that coincident circular Maldacena-Wilson loops are described by a Gaussian matrix model. We report on a novel, supporting two-loop test, but also explain and illustrate why the existing arguments in favor of the conjecture are flawed.