’t Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate

Yamaguchi, Satoshi

doi:10.1007/jhep01(2019)014

Cited by 23 publications

(17 citation statements)

References 48 publications

(79 reference statements)

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“…This agrees with what was found by [18]. This implies that a confining vacuum with mass gap, with no condensate formation and with unbroken ψ 6 , is not consistent.…”

Section: N F =supporting

confidence: 89%

“…A similar reinterpretation of the W and Z bosons is also straightforward. 12 In this respect we differ from the interpretation given in [18]. Indeed there is a long history of studies in strongly interacting chiral gauge theories based on such ideas, starting from [24].…”

Section: N F =mentioning

confidence: 90%

“…Let us further restrict ourselves to SU(6) theory with a single left-handed fermion in the representation, 20. This model was considered recently in [18]. A good part of the analysis below indeed overlaps with [18]; nevertheless, we discuss this simplest model with certain care, in order to fix the ideas, to recall the basic techniques and notations, and to discuss physic questions involved.…”

Section: N F =mentioning

confidence: 99%

“…Other than this, the information we possess at the moment is unfortunately not powerful enough to indicate in more detail the infrared physics of this system. 18 6.2 SU (8) theory with 36 ⊕ 3 × 28 * The classical continuous favor symmetry of this model is…”

Section: Qcd With Quarks In a Two-index Representationmentioning

confidence: 99%

“…the two representation are equivalent because a U(1) ψχ transformation takes the former to the latter. 18 Just for completeness, let us comment also on the conventional matching condition for the discrete 4 symmetry, independently of the 4 − C 2 mixed anomalies discussed above. If 4 is to remain unbroken in the infrared, (3.20) requires for N = 4, that A IR −A UV = 0 mod 4.…”

Section: Qcd With Quarks In a Two-index Representationmentioning

confidence: 99%

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Gauging 1-form center symmetries in simple SU(N) gauge theories

2020

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Consequences of gauging exact C k center symmetries in several simple SU (N ) gauge theories, where k is a divisor of N , are investigated. Models discussed include: the SU (N ) gauge theory with N f copies of Weyl fermions in self-adjoint single-column antisymmetric representation, the well-discussed adjoint QCD, QCDlike theories in which the quarks are in a two-index representation of SU (N ), and a chiral SU (N ) theory with fermions in the symmetric as well as in anti-antisymmetric representations but without fundamentals. Mixed 't Hooft anomalies between the 1-form C k symmetry and some 0-form (standard) discrete symmetry provide us with useful information about the infrared dynamics of the system. In some cases they give decisive indication to select only few possiblities for the infrared phase of the theory.Recently the ideas of generalized symmetries and higher-form gauging have been applied to gain deeper insights on the infrared dynamics of some strongly-coupled 4D gauge theories [1]- [20]. One of the key issues, which lead to many interesting consequences, is the so-called C N center symmetry 1 in SU(N) theories. Although the idea itself is a familiar one, 2 it becomes more powerful when combined with the idea of "gauging" such a discrete center

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“…This agrees with what was found by [18]. This implies that a confining vacuum with mass gap, with no condensate formation and with unbroken ψ 6 , is not consistent.…”

Section: N F =supporting

confidence: 89%

Section: N F =mentioning

confidence: 90%

Section: N F =mentioning

confidence: 99%

Section: Qcd With Quarks In a Two-index Representationmentioning

confidence: 99%

Section: Qcd With Quarks In a Two-index Representationmentioning

confidence: 99%

See 3 more Smart Citations

Gauging 1-form center symmetries in simple SU(N) gauge theories

2020

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BCF anomaly and higher-group structure in the low energy effective theories of mesons

Nakajima

Sakai

Yokokura

2023

J. High Energ. Phys.

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We discuss the BCF anomaly of massless QCD-like theories, first obtained by Anber and Poppitz, from the viewpoint of the low energy effective theories. We assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking due to a quark bilinear condensate. Using the ’t Hooft anomaly matching condition for the BCF anomaly, we find that the low energy effective action is composed of a chiral Lagrangian and a Wess-Zumino-Witten term together with an interaction term of the η′ meson with the background gauge field for a discrete one-form symmetry. It is shown that the low energy effective action cancels the quantum inconsistencies associated with η′ due to an ambiguity of how to uplift the action to a five-dimensional spacetime with a boundary. The η′ term plays a substantial role in exploring the emergent higher-group structure at low energies.

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Vacuum structure of charge k two-dimensional QED and dynamics of an anti D-string near an O1−-plane

Armoni

Sugimoto

2019

J. High Energ. Phys.

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We study the vacuum structure of N f flavour two-dimensional QED with an arbitrary integer charge k. We find that the axial symmetry is spontaneously broken from Z kN f to Z N f due to the non-vanishing condensate of a flavour singlet operator, resulting in k degenerate vacua. An explicit construction of the k vacua is given by using a non-commutative algebra obtained as a central extension of the Z kN f discrete axial symmetry and Z k 1-form (center) symmetry, which represents the mixed 't Hooft anomaly between them.We then give a string theory realization of such a system with k = 2 and N f = 8 by putting an anti D-string in the vicinity of an orientifold O1 − -plane and study its dynamics using the twodimensional gauge theory realized on it. We calculate the potential between the anti D-string and the O1 − -plane and find repulsion in both weak and strong coupling regimes of the two-dimensional gauge theory, corresponding to long and short distances, respectively. We also calculate the potential for the (Q, −1)-string (the bound state of an anti D-string and Q fundamental strings) located close to the O1 − -plane. The result is non-perturbative in the string coupling. 4 dim massless QCD. † The case with N f = 1 is studied in [1], in which case the vacuum structure is similar to that of 4 dim N = 1 SU (N ) SYM, where U (1) A is broken to Z 2N by anomaly and further broken spontaneously to Z 2 , resulting in N vacua. * See [27] for the normal-ordering prescription. † See, e.g., [20] for a review. * These cusp singularities exist even for k = 1. The existence of the cusps can be understood from the mixed anomaly between the vector-like flavour symmetry SU (N f ) V /(Z N f ) V and the charge conjugation symmetry discussed in [21]. We thank the anonymous referee for pointing this out to us. † The overall factor in (2.71) is different from the expression for the energy density given in [28]. In [28], only the contribution from the fermion mass term is taken into account. We found that the kinetic term also has a contribution of the same order and included in (2.71). See Appendix B.2 for details.

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’t Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate

Cited by 23 publications

References 48 publications

Gauging 1-form center symmetries in simple SU(N) gauge theories

Gauging 1-form center symmetries in simple SU(N) gauge theories

BCF anomaly and higher-group structure in the low energy effective theories of mesons

Vacuum structure of charge k two-dimensional QED and dynamics of an anti D-string near an O1−-plane

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