2017
DOI: 10.1007/jhep09(2017)137
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θ =π in S U N / ℤ N $$ \mathrm{S}\mathrm{U}(N)/{\mathbb{Z}}_N $$ gauge theories

Abstract: In SU(N ) gauge theory, it is argued recently that there exists a "mixed anomaly" between the CP symmetry and the 1-form Z N symmetry at θ = π, and the anomaly matching requires CP to be spontaneously broken at θ = π if the system is in the confining phase. In this paper, we elaborate on this discussion by examining the large volume behavior of the partition functions of the SU(N )/Z N theory on T 4à la 't Hooft. The periodicity of the partition function in θ, which is not 2π due to fractional instanton number… Show more

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Cited by 21 publications
(17 citation statements)
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References 37 publications
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“…(28) By construction, this variation vanishes for any field configuration; thus after an integration by parts, and using the definition of the flux tensor (27) we conclude that…”
Section: B the Field Equations Are Conservation Lawsmentioning
confidence: 93%
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“…(28) By construction, this variation vanishes for any field configuration; thus after an integration by parts, and using the definition of the flux tensor (27) we conclude that…”
Section: B the Field Equations Are Conservation Lawsmentioning
confidence: 93%
“…Interestingly, the symmetry principle behind the conservation of such a higher-form currents has only recently been studied systematically, and is called a generalized global symmetry [21]. Such symmetries have found applications in diverse physical contexts, ranging from constraining the phase structure of gauge theories and topological phases [22][23][24][25][26][27][28] to an understanding of gauge bosons as Goldstone modes [21,29,30] to symmetry-based formulations of hydrodynamics [13,[31][32][33][34][35][36]. The realization of the generalized global symmetry associated with the conservation of magnetic flux will be a technical tool in our analysis (we call it the "magnetic photon shift"); for now we simply note that the source for the 2-form current J µν is a fixed 2-form classical field that we call b µν .…”
Section: A Microscopic Symmetries Of the Systemmentioning
confidence: 99%
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“…Therefore by considering the mixed 't Hooft anomaly of the center symmetry, one may find constraints of the phase structure of the theory in the confining phase. There has been interesting progress along this line [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21].…”
Section: Introductionmentioning
confidence: 99%
“…A comment on spontaneous CP breaking In an SU(N ) gauge theory with θ π, under several conditions, there can be a spontaneous CP breaking where the first derivative of the partition function with respect to θ is non-vanishing [111][112][113][114]. It is discussed in Ref.…”
Section: Discussionmentioning
confidence: 99%