Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT

TL;DR

This paper explores how electromagnetic duality in AdS/CFT exchanges boundary conditions, gauges global symmetries, and realizes 2-group symmetries holographically, with explicit renormalization and generalizations to other fields and dimensions.

Contribution

It demonstrates how dualizing 1-form to 2-form fields in AdS$_5$ induces 2-group symmetries in the dual field theory, extending the understanding of generalized symmetries holographically.

Findings

Dualization exchanges boundary conditions and gauges global $U(1)$ symmetry.

Holographic renormalization confirms the emergence of 2-group symmetry.

Generalization to other rank fields and dimensions is discussed.

Abstract

We discuss how electromagnetically dualizing a 1-form to a 2-form in AdS$_5$ exchanges regular and alternate boundary conditions, and thus gauges the originally global $U(1)$ symmetry in the dual field theory. The generalized symmetry current dual to the 2-form in the bulk is identified as the dual field strength of the gauged $U(1)$, and the associated double-trace operator with a logarithmically running coupling is just the gauged $U(1)$ Maxwell action. Applying this dualization to an AdS Maxwell-Chern-Simons theory dual to a global $U(1) \times U(1)$ model with an 't Hooft anomaly results in a theory with a modified field strength that holographically realizes a 2-group symmetry. We explicitly carry out the holographic renormalization to verify this, and discuss the generalization to other rank fields in other dimensions.