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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  

Preprint Link:  https://arxiv.org/abs/1802.09512v2 (pdf) 
Date accepted:  20190108 
Date submitted:  20181116 01:00 
Submitted by:  Hofman, Diego 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

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 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.
Published as SciPost Phys. 6, 006 (2019)
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 20181217 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1802.09512v2, delivered 20181217, doi: 10.21468/SciPost.Report.749
Strengths
1The paper is written clearly, the key results are well emphasized.
2The topic is of current interest.
3The results suggest several potential future directions.
Weaknesses
I could not find any.
Report
The paper discusses the extension of Goldstone's theorem to pform symmetries. It is shown that if charged pdimensional objects follow a perimeter law then the theory has a Goldstone mode. For CFT's with pform symmetry in dimension d=2(p+1), correlation functions of the higherform current can be realized in terms of a free Goldstone mode. Moreover, there is an infinite number of conserved charges, which are shown to lead to a higherform generalization of the KacMoody algebra. In 4 dimensions, the construction is formulated using twistor formalism. The results are intriguing and suggest several generalizations for future research on the topic. The paper has a clear structure, and the essential concepts are introduced in a transparent and insightful way.
Requested changes
None.
Anonymous Report 1 on 2018127 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1802.09512v2, delivered 20181207, doi: 10.21468/SciPost.Report.717
Strengths
The paper is clearly written, and it contains many important results, on topics of current interest to the community.
Weaknesses
None that I noticed.
Report
The paper extends Goldstone's theorem to higherform symmetries. It moreover shows that oneform symmetries in a 4d CFT can be photonized to free Maxwell electrodynamics and, more generally, that pform symmetries in a CFT in 2(p+1) dimensions has a free realization. In the 4d case, infinitely many conserved 0form charges are studied by a twisterbased formalism and it is shown that the charge algebra has central extension, giving an analog of 2d KacMoody algebra for higher form symmetries. All of these results are interesting, and give new insights into higherform symmetry. The paper is terse in a good way  it is very clear and packed with nice results and insights. I am recommending Tier II below just because I do not know how to calibrate the level for an Editor's selection, and I think that this paper's readership might be more limited and specialized as compared with the top 10% level Editor's Select.
Requested changes
none