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

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) x U(1) model with a '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.

Automated summary

In this discussion, the electromagnetic dualization of 1-form to a 2-form in AdS(5) is shown to exchange regular and alternate boundary conditions, thereby gauging the originally global U(1) symmetry in the dual field theory. This method is then applied to a Maxwell-Chern-Simons theory in AdS, resulting in a theory with a modified field strength that holographically realizes a 2-group symmetry. The holographic renormalization is explicitly carried out to verify the results, and the potential generalization to other rank fields in different dimensions is also discussed.