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Goldstone modes and photonization for higher form symmetries
by Diego M. Hofman, Nabil Iqbal
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Submission summary
Authors (as registered SciPost users): | Diego Hofman · Nabil Iqbal |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/1802.09512v2 (pdf) |
Date accepted: | Jan. 8, 2019 |
Date submitted: | Nov. 16, 2018, 1 a.m. |
Submitted by: | Hofman, Diego |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
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Approach: | Theoretical |
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 $CFT_4$ 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.
Published as SciPost Phys. 6, 006 (2019)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2018-12-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1802.09512v2, delivered 2018-12-17, doi: 10.21468/SciPost.Report.749
Strengths
2-The topic is of current interest.
3-The results suggest several potential future directions.
Weaknesses
Report
Requested changes
None.
Report #1 by Anonymous (Referee 1) on 2018-12-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1802.09512v2, delivered 2018-12-07, doi: 10.21468/SciPost.Report.717
Strengths
Weaknesses
Report
Requested changes
none