SciPost Phys. 6, 006 (2019) ·
published 14 January 2019

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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
1form 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 0form charges that are constructed by integrating the symmetry
currents against suitable 1forms. We study these charges by developing a
twistorbased 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 KacMoody algebra for
higher form symmetries.
SciPost Phys. 4, 005 (2018) ·
published 29 January 2018

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We study the holographic duals of fourdimensional field theories with 1form
global symmetries, both discrete and continuous. Such higherform 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 nonconformal field
theory with a marginally running doubletrace coupling. We explore its
hydrodynamic behavior at finite temperature and make contact with recent
symmetrybased 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 ChernSimons description: we
clarify the conventional 0form case and work out the 1form case. Depending on
boundary conditions, such discrete symmetries may be embedded in continuous
higherform symmetries that are spontaneously broken. We study the resulting
boundary Goldstone mode, which in the 1form 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 ChernSimons terms put together. We work out the operator content
and demonstrate the existence of new backreacted anisotropic scaling solutions
that carry higherform charge.