Wilson Surface One-Point Functions: A Case Study

TL;DR

This paper computes holographic one-point functions for Wilson surfaces with complex shape dependence, using analytical and numerical methods, and explores the effects of averaging over membrane moduli space.

Contribution

It introduces a detailed analysis of Wilson surface one-point functions for toroidal and cylindrical surfaces, highlighting shape dependence and the role of moduli space averaging.

Findings

One-point functions depend intricately on surface shape and position.

Averaging over membrane moduli space is crucial for accurate computations.

Both analytical and numerical results are provided for different surface geometries.

Abstract

We compute holographic one-point functions for Wilson surfaces in the case of a toroidal surface operator. Compared to the cases of a planar or spherical surface operator, these one-point functions exhibit a more intricate dependence on the shape and position of both the surface and the local operators. Averaging over the moduli space of membranes dual to the surface operator plays a key role in the computations. We obtain both analytical and numerical results. The case of a cylindrical surface operator is also studied.