We discuss generalized global symmetries and their breaking. We extend Goldstone's theorem to higher form symmetries by showing that a perimeter law for an extended $p$-dimensional defect operator charged under a continuous $p$-form generalized global symmetry necessarily results in a gapless mode in the spectrum. We also show that a $p$-form symmetry in a conformal theory in $2(p+1)$ dimensions has a free realization. In four dimensions this means any 1-form symmetry in a $CFT_4$ can be realized by free Maxwell electrodynamics, i.e. the current can be photonized. The photonized theory has infinitely many conserved 0-form charges that are constructed by integrating the symmetry currents against suitable 1-forms. We study these charges by developing a twistor-based formalism that is a 4d analogue of the usual holomorphic complex analysis familiar in $CFT_2$. The charges are shown to obey an algebra with central extension, which is an analogue of the 2d Abelian Kac-Moody algebra for higher form symmetries.
Cited by 5
Jay Armas et al., Magnetohydrodynamics as Superfluidity
Phys. Rev. Lett. 122, 141603 (2019) [Crossref]
Noriyuki Sogabe et al., Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries
Phys. Rev. D 99, 125003 (2019) [Crossref]
Alexandre Belin et al., Einstein gravity from ANEC correlators
J. High Energ. Phys. 2019, 32 (2019) [Crossref]
Xiao-Gang Wen, Emergent anomalous higher symmetries from topological order and from dynamical electromagnetic field in condensed matter systems
Phys. Rev. B 99, 205139 (2019) [Crossref]
Samuel E. Gralla et al., Effective field theory of force-free electrodynamics
Phys. Rev. D 99, 105004 (2019) [Crossref]
Ontology / TopicsSee full Ontology or Topics database.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Diego Hofman,
- 2 Nabil Iqbal