Abstract
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.
Highlights
We study the holographic duals of four-dimensional field theories with 1-form global symmetries, both discrete and continuous
This fact allows for the large number of constructions of local theories enjoying 0-form symmetries: because particles are the quanta of local fields, there is always a quantum field theory description available for these systems
We could equivalently have formulated the theory in terms of a magnetic photon Am, in which case we would have concluded that Jm ∼ dAm as a consequence of the absence of electric charges; in the free photon phase of Maxwell electrodynamics both generalized global symmetries are spontaneously broken
Summary
We will discuss the manifestation of generalized global symmetries in d-dimensional quantum field theories with holographic duals. For familiar 0-form symmetries these objects have a 1-dimensional world-volume and we conclude that particles are the natural charged objects of 0-form symmetries This fact allows for the large number of constructions of local theories enjoying 0-form symmetries: because particles are the quanta of local fields, there is always a quantum field theory description available for these systems. The advantage of recasting the theory of extended objects in quantum field theory language comes, at a price: the introduction of unphysical symmetries in the form of a gauge group and gauge constraints in the Hilbert space of states This fact obscures substantially the role of the physical symmetries that we were interested in in the first place. The recent paper [5] studies generalized symmetry in holography from the point of view of magnetohydrodynamic applications
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