| Summary: | We study the holographic duals of four-dimensional field theories with 1-form
global symmetries, both discrete and continuous. Such higher-form global
symmetries are associated with antisymmetric tensor gauge fields in the bulk.
Various different realizations are possible: we demonstrate that a Maxwell
action for the bulk antisymmetric gauge field results in a non-conformal field
theory with a marginally running double-trace coupling. We explore its
hydrodynamic behavior at finite temperature and make contact with recent
symmetry-based formulations of magnetohydrodynamics. We also argue that
discrete global symmetries on the boundary are dual to discrete gauge theories
in the bulk. Such gauge theories have a bulk Chern-Simons description: we
clarify the conventional 0-form case and work out the 1-form case. Depending on
boundary conditions, such discrete symmetries may be embedded in continuous
higher-form symmetries that are spontaneously broken. We study the resulting
boundary Goldstone mode, which in the 1-form case may be thought of as a
boundary photon. Our results clarify how the global form of the field theory
gauge group is encoded in holography. Finally, we study the interplay of
Maxwell and Chern-Simons terms put together. We work out the operator content
and demonstrate the existence of new backreacted anisotropic scaling solutions
that carry higher-form charge.
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