Higher-group global symmetry and the bosonic M5 brane
arXiv:2402.19458 · doi:10.1007/JHEP08(2024)003
Abstract
Higher-group symmetries are combinations of higher-form symmetries which appear in various field theories. In this paper, we explain how higher-group symmetries arise in 10d and 11d supergravities when the latter are coupled to brane sources. Motivated by this observation, we study field theories at zero and finite temperature invariant under a class of continuous Abelian higher-group symmetries. We restrict the analysis to the low-energy regime where the dynamical field content exclusively consists of Goldstone fields arising from the spontaneous breaking of higher-group and spacetime symmetries. Invariant quantities are constructed and the phases of matter are classified according to the pattern of spontaneous symmetry breaking. With respect to supergravity, we highlight how such Goldstone effective theories provide a symmetry-based interpretation for the theories living on D/M-branes. As an explicit example we construct a 6-group invariant action for the bosonic M5 brane, consistent with the self-duality of the 3-form field strength on the brane. While the self-duality condition in the bosonic case needs to be imposed externally as a constraint at zero temperature, we find an equilibrium effective action for the bosonic M5 brane at finite temperature that inherently implements self-duality.
36 pages. v2: minor text improvements
References in corpus (7)
- Generalized Global Symmetries
- Generalized Symmetries in Condensed Matter
- Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
- Field theories with higher-group symmetry from composite currents
- Approximate higher-form symmetries, topological defects, and dynamical phase transitions
- Hydrodynamic effective field theory and the analyticity of hydrostatic correlators
- Holographic duals of the * gauge theory