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

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.

21 pages, 2 figures. v2: References and small elaborations added, typo corrected

References in corpus (9)

• Generalized Global Symmetries
• Higher-Dimensional Algebra V: 2-Groups
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Holographic renormalization as a canonical transformation
• Higher Gauge Theory: 2-Connections on 2-Bundles
• Higher-form symmetries and 3-group in axion electrodynamics
• Generalized symmetries and holography in ABJM-type theories
• Conformal blocks for AdS5 singletons
• Holography, Duality and Higher-Spin Theories