Non-Abelian Symmetry Operators from Hanging Branes in $AdS_5 \times S^5$

TL;DR

This paper explores how topological operators for non-Abelian symmetries are realized holographically in Type IIB string theory on $AdS_5 imes S^5$, revealing bound states of D5-branes and KK monopoles as symmetry operators.

Contribution

It introduces a holographic construction of non-Abelian symmetry operators using D5-branes and KK monopoles in $AdS_5 imes S^5$, linking them to boundary symmetry representations.

Findings

Bound states of D5-branes and KK monopoles realize symmetry operators.

These bound states account for Gauss' law constraints from flux and gravity.

The D5-KK bound state encodes Wilson line endpoint representations.

Abstract

We investigate the holographic realization of topological operators for continuous non-Abelian symmetries in quantum field theories. As a concrete case study, we focus on Type IIB string theory on $AdS_5 \times S^5$ which admits an $SO(6)$ isometry, dual to the R-symmetry in 4d $N=4$ super Yang-Mills theory. We argue that symmetry operators for continuous symmetries are generally realized by bound states of D5-branes and KK monopoles hanging from the conformal boundary. Together they account for the contributions to the Gauss' law constraints from the self-dual 5-form flux and the Einstein-Hilbert term respectively. We also demonstrate how the D5-KK bound state measures the representation of the endpoint of Wilson lines constructed by D3-branes.