M2-doughnuts

TL;DR

This paper introduces new M2-brane solutions in $AdS_7\times S^4$ for calculating conformally invariant BPS surface operators in the six-dimensional $(2,0)$ theory, providing explicit expectation values at large $N$ and exploring a limiting case resembling Wilson loops.

Contribution

It presents novel M2-brane solutions in $AdS_7\times S^4$ that compute BPS surface operators, extending the understanding of surface observables in the $(2,0)$ theory.

Findings

Explicit finite expectation values at large $N$ for the surface operators.

Identification of a limiting case resembling Wilson loops as a thin torus.

Analysis of the cylinder limit as a surface generalization of Wilson loops.

Abstract

We present a family of new M2-brane solutions in $AdS_7\times S^4$ that calculate toroidal BPS surface operators in the $\mathcal{N}=(2,0)$ theory. These observables are conformally invariant and not subject to anomalies so we are able to evaluate their finite expectation values at leading order at large $N$. In the limit of a thin torus we find a cylinder, which is a natural surface generalization of both the circular and parallel lines Wilson loop. We study and comment on this limit in some detail.