On gravitational description of Wilson lines

TL;DR

This paper characterizes supergravity solutions dual to supersymmetric Wilson lines in N=4 super-Yang-Mills, showing they are determined by a single Laplace equation with boundary conditions linked to brane configurations.

Contribution

It introduces a unique supergravity solution framework for Wilson lines, connecting boundary conditions to brane configurations and topology.

Findings

Solutions are specified by a single Laplace equation in two dimensions.

Regular geometries correspond to specific Dirichlet boundary conditions.

The solutions exhibit nontrivial topologies with non-contractible spheres.

Abstract

We study solutions of Type IIB supergravity, which describe the geometries dual to supersymmetric Wilson lines in N=4 super-Yang-Mills. We show that the solutions are uniquely specified by one function which satisfies a Laplace equation in two dimensions. We show that if this function obeys a certain Dirichlet boundary condition, the corresponding geometry is regular, and we find a simple interpretation of this boundary condition in terms of D3 and D5 branes which are dissolved in the geometry. While all our metrics have AdS_5 x S^5 asymptotics, they generically have nontrivial topologies, which can be uniquely specified by a set of non-contractible three- and five-spheres.