Goldstone modes and photonization for higher form symmetries

Hofman, Diego M.; Iqbal, Nabil

doi:10.21468/SciPostPhys.6.1.006

Goldstone modes and photonization for higher form symmetries

Diego M. Hofman
(
- Amsterdam U.
)
,
Nabil Iqbal
(
- Durham U., CPT
)

Feb 26, 2018

7 pages

Published in:

SciPost Phys. 6 (2019) 1, 006

Published: Jan 14, 2019

e-Print:

1802.09512 [hep-th]

DOI:

10.21468/SciPostPhys.6.1.006 (publication)

View in:

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Abstract: (SciPost Fundation)

We discuss generalized global symmetries and their breaking. We extendGoldstone's theorem to higher form symmetries by showing that a perimeter lawfor an extended

p

-dimensional defect operator charged under a continuous

p

-form generalized global symmetry necessarily results in a gapless mode inthe 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 any1-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 manyconserved 0-form charges that are constructed by integrating the symmetrycurrents against suitable 1-forms. We study these charges by developing atwistor-based formalism that is a 4d analogue of the usual holomorphic complexanalysis familiar in

CFT_2

. The charges are shown to obey an algebra withcentral extension, which is an analogue of the 2d Abelian Kac-Moody algebra forhigher form symmetries.

Note:

7 pages, 1 figure. v2. Added reference and minor clarifications. v3. Acknowledgment added

symmetry: global
algebra: Kac-Moody
dimension: 4
dimension: 2
any-dimensional
differential forms: 1
Goldstone theorem
twistor
Wilson loop
correlation function

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