Generalized global symmetries and holography

TL;DR

This paper explores the holographic duals of four-dimensional theories with higher-form global symmetries, revealing new insights into their bulk gauge fields, boundary modes, and the interplay of Maxwell and Chern-Simons terms.

Contribution

It provides a comprehensive analysis of holographic duals for higher-form symmetries, including bulk gauge descriptions, boundary Goldstone modes, and novel anisotropic solutions.

Findings

Bulk Maxwell action leads to non-conformal theories with marginal couplings.

Discrete boundary symmetries correspond to bulk discrete gauge theories with Chern-Simons terms.

New anisotropic scaling solutions carrying higher-form charge are demonstrated.

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.