Continuous symmetries and charge measurement of boundary operators in holography

TL;DR

This paper explores how continuous symmetries are measured in holography, using boundary operators, Wilson lines, and U-shaped defects, with explicit string theory examples and analysis of brane dynamics.

Contribution

It introduces a universal low-energy framework for charge measurement in holography and provides explicit top-down string theory realizations with detailed brane dynamics.

Findings

Universal features of charge measurement derived from low-energy perspective

Explicit Type IIB and M-theory realizations with Abelian and non-Abelian symmetries

Analysis of brane dynamics and topological nature of hanging brane configurations

Abstract

We study holographic charge measurement for continuous internal symmetries. Charged boundary operators are characterized by Wilson lines of bulk gauge fields ending on the boundary, while charge measurement is performed using U-shaped defects hanging from the boundary. We derive universal features of this process from a low-energy point of view, and show how the hanging defect picture mimics the thickening regularization of continuous symmetry operators in field theory. Furthermore, we provide explicit top-down realizations in AdS/CFT setups in Type IIB string theory and M-theory, featuring Abelian as well as non-Abelian symmetries. In the case of Type IIB constructions, we analyze the brane dynamics underlying the charge measurement process. Along the way, we also characterize how hanging brane configurations can be regarded as being topological, and demonstrate how tachyon dynamics account for their fusion rules.