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Durham University

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Publication details for Nabil Iqbal

Hofman, Diego & Iqbal, Nabil (2019). Goldstone modes and photonization for higher form symmetries. SciPost Physics 6(1): 006.

Author(s) from Durham

Abstract

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 C F T4 can be realized by free
Maxwell electrodynamics, i.e. the current can be photonized. The 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
C F T2
. 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.