Metric Isometries, Holography, and Continuous Symmetry Operators

TL;DR

This paper explores the duality between topological symmetry operators in boundary CFTs and dynamical branes in the bulk AdS space, revealing new insights into the geometric and physical nature of these symmetries.

Contribution

It provides a detailed analysis of continuous symmetries in AdS/CFT, identifying their dual brane configurations as metric singularities and describing their properties and implications.

Findings

Topological symmetry operators correspond to dynamical branes associated with metric singularities.

These branes are related to Gukov-Witten-like vortex configurations in the bulk.

The properties of these branes are determined by bulk dynamics and can be generalized beyond semi-classical gravity.

Abstract

In the AdS/CFT correspondence, a topological symmetry operator of the boundary CFT is dual to a dynamical brane in the gravitational bulk. Said differently, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the "internal" factor $X$ of $\text{AdS}\times X$. In the extra-dimensional geometry, these branes are associated with various metric singularities and do not arise from wrapped D-branes. Boosts relate configurations interpreted as topological symmetry operators and heavy defects in the CFT. From the perspective of the AdS factor, with gravity and bulk gauge fields, these are codimension two Gukov-Witten-like vortex configurations which are the gravity duals of 0-form symmetry operators. These effective branes come with an asymptotic tension and size which is also fully fixed by bulk dynamics. We use this higher-dimensional perspective to determine properties of the worldvolume theory for these branes. We also discuss how these considerations generalize to more general QFTs engineered via string theory which need not possess a semi-classical gravity dual.