Holographic Interface-Particle Potential

TL;DR

This paper compares the potential energy between an interface and a test particle in N=4 supersymmetric gauge theories and their gravity dual, confirming the agreement between gauge theory calculations and string theory predictions.

Contribution

It demonstrates the matching of potential energy calculations from gauge theory and gravity duals for an interface in N=4 supersymmetric theories, using Wilson loops and string actions.

Findings

Gauge theory and gravity calculations agree on the potential energy.

The Wilson loop expectation value matches the on-shell string action.

The fuzzy funnel solution effectively describes the interface in both frameworks.

Abstract

We consider two N=4 supersymmetric gauge theories connected by an interface and the gravity dual of this system. This interface is expressed by a fuzzy funnel solution of Nahm's equation in the gauge theory side. The gravity dual is a probe D5-brane in AdS_5 x S^5. The potential energy between this interface and a test particle is calculated in both the gauge theory side and the gravity side by the expectation value of a Wilson loop. In the gauge theory it is evaluated by just substituting the classical solution to the Wilson loop. On the other hand it is done by the on-shell action of the fundamental string stretched between the AdS boundary and the D5-brane in the gravity. We show the gauge theory result and the gravity one agree with each other.