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Generalized global symmetries and holography

Hofman, Diego; Iqbal, Nabil

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Diego Hofman


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.


Hofman, D., & Iqbal, N. (2018). Generalized global symmetries and holography. SciPost Physics, 4(1), Article 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
Publisher SciPost
Peer Reviewed Peer Reviewed
Volume 4
Issue 1
Article Number 005
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