Vacuum structure of bifundamental gauge theories at finite topological angles

Tanizaki, Yuya; Kikuchi, Yuta

doi:10.1007/jhep06(2017)102

Cited by 92 publications

(104 citation statements)

References 96 publications

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“…Thus, the shift θ YM → θ YM + 2π/p (⇔θ →θ + 2π) gives the extra phase of the partition function by 24) and the overall Z N p phase is characterized by the background gauge fields. When θ YM is quantized in an odd-integer multiple of π/p (half of its domain 2π/p), this relation can be used to obtain the mixed 't Hooft anomaly or the global inconsistency between CP symmetry and Z [1] N× Z [3] p , generalizing [21][22][23][24]68] to cases involving 4-group symmetry. Recently, this type of relation (for 1-form symmetry) itself is understood as the generalized 't Hooft anomaly with the θ-angle periodicity [69], and it naturally leads to the existence of multi-branch structure as will be discussed in the following subsections.…”

Section: Mixed Anomaly Between Z [1]mentioning

confidence: 99%

Modified instanton sum in QCD and higher-groups

Tanizaki¹,

Ünsal²

2020

J. High Energ. Phys.

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121

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We consider the SU (N ) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p. We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2πperiodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only Z N 1-form symmetry but also Z p 3-form symmetry, and we study the global nature of this theory from the recent 't Hooft anomaly matching. The computation of 't Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-N and also the reliable semiclassics on R 3 × S 1 , and we find that the topological susceptibility plays a role of the order parameter for the Z p 3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by Z p , and it leads to the extra p vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the 't Hooft anomaly.

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Section: Mixed Anomaly Between Z [1]mentioning

confidence: 99%

Modified instanton sum in QCD and higher-groups

Tanizaki¹,

Ünsal²

2020

J. High Energ. Phys.

Self Cite

121

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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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“…This vacuum structure has recently been clarified for finite N by the identification of a mixed discrete 't Hooft anomaly for T-symmetry and a 1-form center symmetry [5] (See also [6][7][8]). The presence of this anomaly, along with the assumption of a gapped spectrum, provides a more general argument for the spontaneous breaking of T-symmetry and the presence of degenerate vacua atθ ¼ π.…”

Section: Introductionmentioning

confidence: 99%

Domain wall moduli in softly-broken SQCD at θ¯=π

Ritz

Shukla

2018

Phys. Rev. D

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We analyze the moduli space dynamics of domain walls in SUðNÞ QCD atθ ¼ π, by softly breaking N ¼ 1 SQCD with sfermion mixing. In the supersymmetric limit, BPS domain walls between neighboring vacua are known to possess nontranslational flavor moduli that form a CP N−1 sigma model. For the simplest case with gauge group SUð2Þ and N f ¼ 2, we show that this sigma model also exhibits a Hopf term descending from the bulk Wess-Zumino term with a quantized coefficient. On soft-breaking of supersymmetry via sfermion mixing that preserves the flavor symmetry, these walls and their moduli-space dynamics survives whenθ ¼ π so that there are two degenerate vacua.

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Vacuum structure of bifundamental gauge theories at finite topological angles

Cited by 92 publications

References 96 publications

Modified instanton sum in QCD and higher-groups

Modified instanton sum in QCD and higher-groups

Undoing decomposition

Domain wall moduli in softly-broken SQCD at θ¯=π

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