Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking

Tanizaki, Yuya

doi:10.1007/jhep08(2018)171

Cited by 80 publications

(87 citation statements)

References 70 publications

(110 reference statements)

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“…Therefore, if c,f,B can be found to satisfy conditions (i) to (iii), then it is always trivial to find G ∈ Z that satisfies condition (iv). 9 Notice that gauge invariant composites have c = 1 in the vectorlike theories we consider: using D c IR = 0, since the composites are color singlets, we have c =…”

Section: Anomalies In the Background Of Bcf Fluxes On Cpmentioning

confidence: 99%

“…The study of these generalized anomalies is a currently active area of research with contributions coming from the high-energy, condensed matter, and mathematical communities. We do not claim to be in command of all points of view and only give a list of references written from a (largely) high-energy physics perspective and pertaining to theories somewhat similar to the ones discussed in this paper [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

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confidence: 99%

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Generalized ’t Hooft anomalies on non-spin manifolds

Anber

Poppitz

2020

J. High Energ. Phys.

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We study the mixed anomaly between the discrete chiral symmetry and general baryon-color-flavor (BCF) backgrounds in SU (N c ) gauge theories with N f flavors of Dirac fermions in representations R c of N -ality n c , formulated on non-spin manifolds. We show how to study these theories on CP 2 by turning on general BCF fluxes consistent with the fermion transition functions. We consider several examples in detail and argue that matching the anomaly on non-spin manifolds places stronger constraints on the infrared physics, compared to the ones on spin manifolds (e.g. T 4 ). We also show how to consistently formulate various chiral gauge theories on non-spin manifolds.

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Section: Anomalies In the Background Of Bcf Fluxes On Cpmentioning

confidence: 99%

mentioning

confidence: 99%

Generalized ’t Hooft anomalies on non-spin manifolds

Anber

Poppitz

2020

J. High Energ. Phys.

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“…We should mention that there has recently been a great deal of interest in gauging oneform symmetries in other dimensions, see for example [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Undoing decomposition

Sharpe

2019

Int. J. Mod. Phys. A

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In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition -an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov-Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such gaugings explicitly in examples involving orbifolds, nonsupersymmetric pure Yang-Mills theories, and supersymmetric gauge theories in two dimensions. Along the way, we learn explicit concrete details of the topological configurations that path integrals sum over when gauging a one-form symmetry, and we also uncover 'hidden' one-form symmetries.

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“…Yet, if we have N f flavors, then the faithful group that acts on the fermions is SU (N c ) × SU (N f )/Z n , where n = gcd(N c , N f ). Therefore, one may gauge the center-flavor symmetry Z n , which can lead to constraints on the IR dynamics [17]; see also [18][19][20] for similar constructions.…”

Section: Introductionmentioning

confidence: 99%

On the baryon-color-flavor (BCF) anomaly in vector-like theories

Anber

Poppitz

2019

J. High Energ. Phys.

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We consider the most general fractional background fluxes in the color, flavor, and baryon number directions, compatible with the faithful action of the global symmetry of a given theory. We call the obstruction to gauging symmetries revealed by such backgrounds the baryon-color-flavor (BCF) 't Hooft anomaly. We apply the BCF anomaly to vector-like theories, with fermions in higher-dimensional representations of arbitrary N-ality, and derive non-trivial constraints on their IR dynamics. In particular, this class of theories enjoys an independent discrete chiral symmetry and one may ask about the fate of this symmetry in the background of BCF fluxes. We show that, under certain conditions, an anomaly between the chiral symmetry and the BCF background rules out massless composite fermions as the sole player in the IR: either the composites do not form or additional contributions to the matching of the BCF anomaly are required. We can also give a flavor-symmetric mass to the fermions, smaller than or of order the strong scale of the theory, and examine the θ-angle periodicity of the theory in the BCF background. Interestingly, we find that the conditions that rule out the composites are the exact same conditions that lead to an anomaly of the θ periodicity: the massive theory will experience a phase transition as we vary θ from 0 to 2π. arXiv:1909.09027v2 [hep-th]

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Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking

Cited by 80 publications

References 70 publications

Generalized ’t Hooft anomalies on non-spin manifolds

Generalized ’t Hooft anomalies on non-spin manifolds

Undoing decomposition

On the baryon-color-flavor (BCF) anomaly in vector-like theories

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