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.
Highlights
Symmetries are a fundamental aspect of physics, and their association with conserved charges and currents is a deep principle
An elementary example occurs with a Uð1Þ gauge field in four dimensions, where the dual field strength behaves as a two-index generalized current that is conserved in the absence of magnetic sources due to the Bianchi identity
Dumitrescu and Intriligator have described how gauging certain global symmetries with ’t Hooft anomalies leads to a generalized symmetry that for consistency must transform nontrivially under ordinary symmetries of the theory, producing a so-called 2-group structure [2]
Summary
Symmetries are a fundamental aspect of physics, and their association with conserved charges and currents is a deep principle. After going through the case of the 1-form and the 2-form in AdS5 in some detail, we show how the statement that electromagnetic duality in AdS exchanges regular and alternate boundary conditions, and gauges the dual global symmetry, holds for general rank p-forms in general dimension This is the gravity dual of the statement that gauging any conserved generalized symmetry produces a new generalized symmetry from the Bianchi identity of the new dynamical gauge field. Doubletrace boundary conditions are possible given an appropriate choice of finite counterterm, which we identity as the Maxwell action for this dynamical Uð1Þ
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