Generalized global symmetries and holography

Hofman, Diego; Iqbal, Nabil

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.

Citation

Hofman, D., & Iqbal, N. (2018). Generalized global symmetries and holography. SciPost Physics, 4(1), Article 005. https://doi.org/10.21468/scipostphys.4.1.005

• Journal Article Type: Article
• Acceptance Date: Jan 18, 2018
• Online Publication Date: Jan 29, 2018
• Publication Date: Jan 29, 2018
• Deposit Date: Jan 31, 2018
• Publicly Available Date: Mar 7, 2018
• Journal: SciPost Physics.
• Print ISSN: 2542-4653
• Electronic ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 1
• Article Number: 005
• DOI: https://doi.org/10.21468/scipostphys.4.1.005
• Public URL: https://durham-repository.worktribe.com/output/1367438
• Related Public URLs: https://arxiv.org/abs/1707.08577