't Hooft Operators on an Interface and Bubbling D5-Branes

TL;DR

This paper studies supersymmetric brane configurations involving D5, D1, and D3-branes in AdS_5 x S^5, revealing bubbling behavior and proposing a dictionary linking Young diagrams to D5-brane setups for 't Hooft operators.

Contribution

It derives differential equations for supersymmetric configurations and establishes a novel correspondence between Young diagrams and probe D5-brane geometries.

Findings

Supersymmetric conditions lead to bubbling solutions.

Differential equations characterize the probe D5-brane configurations.

A proposed dictionary links Young diagrams to brane setups.

Abstract

We consider a brane configuration consisting of a D5-brane, D1-branes and D3-branes. According to the AdS/CFT correspondence this system realizes a 't Hooft operator embedded in the interface in the gauge theory side. In the gravity side the near-horizon geometry is AdS_5 x S^5. The D5-brane is treated as a probe in the AdS_5 x S^5 and the D1-branes become the gauge flux on the D5-brane. We examine the condition for preserving appropriate amount of supersymmetry and derive a set of differential equations which is the sufficient and necessary condition. This supersymmetric configuration shows bubbling behavior. We try to derive the relation between the probe D5-brane and the Young diagram which labels the corresponding 't Hooft operator. We propose the dictionary of the correspondence between the Young diagram and the probe D5-brane configuration.