We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Research & business

View Profile

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


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.