From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling

Yamazaki, Masahito; Yonekura, Kazuya

doi:10.1007/jhep07(2017)088

Cited by 56 publications

(60 citation statements)

References 112 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that, applying the discussion of Ref. [96], we can obtain more explicit connection between generalized YM theory on T 3 × R with 't Hooft flux and the charge-p CP N −1 model on R × S 1 with Z N twisted boundary condition. The p = 1 version of the twisted CP N −1 model was proposed to show the volume independence in Refs.…”

Section: Connection Between Modified Instanton Sums In 4d and 2dmentioning

confidence: 65%

Modified instanton sum in QCD and higher-groups

Tanizaki¹,

Ünsal²

2020

J. High Energ. Phys.

121

View full text Add to dashboard Cite

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.

show abstract

Section: Connection Between Modified Instanton Sums In 4d and 2dmentioning

confidence: 65%

Modified instanton sum in QCD and higher-groups

Tanizaki¹,

Ünsal²

2020

J. High Energ. Phys.

121

View full text Add to dashboard Cite

show abstract

“…Deconfinement means that hmjΩi ¼ 0 for m ≠ 0. This criterion of (de) confinement might be supported by an analytical picture of confinement [30]. Intuitively, confinement means (see, e.g., [8]) that the gauge field and, in particular, W T is quantum mechanically well fluctuating.…”

Section: -Form N Cmentioning

confidence: 97%

“…Due to this w 2 , there are fractional instantons in X with instanton charge ðm þ∞ − m −∞ Þ=n mod 1 [30] (see also [31]). We remark that explicit instanton solutions are not at all necessary for our discussion, and only the topological data are important.…”

Section: Anomalymentioning

confidence: 99%

Anomaly constraints on deconfinement and chiral phase transition

Shimizu

Yonekura²

2018

Phys. Rev. D

Self Cite

111

109

View full text Add to dashboard Cite

We study the constraints on thermal phase transitions of SUðN c Þ gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless fermions: (i) adjoint fermions and (ii) N f flavors of fundamental fermions with a nontrivial greatest common divisor, gcdðN c ; N f Þ ≠ 1. For the first case (i), we show that the chiral symmetry restoration in terms of the standard Landau-Ginzburg effective action is impossible at a temperature lower than that of deconfinement. For the second case (ii), we introduce a modified version of the center symmetry, which we call centerflavor symmetry, and draw similar conclusions under a certain definition of confinement. Moreover, at zero temperature, our results give a partial explanation of the appearance of dual magnetic gauge groups in (supersymmetric) QCD when gcdðN c ; N f Þ ≠ 1.

show abstract

“…Such discrete anomalies and global inconsistency conditions also appear in lower-dimensional theories and can be used to place interesting constraints on the dynamics of strongly coupled theories. For some recent work on the subject see also[33][34][35][36][37][38]. In addition, four-dimensional gauge theories may enjoy various other discrete anomalies, not of the type we have investigated here.…”

mentioning

confidence: 88%

The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade

Karasik

Komargodski

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the phases of the SU (N 1 ) × SU (N 2 ) gauge theory with a bi-fundamental fermion in 3+1 dimensions. We show that the discrete anomalies and Berry phases associated to the one-form symmetry of the theory allow for several topologically distinct phase diagrams. We identify several limits of the theory where the phase diagram can be determined using various controlled approximations. When the two ranks are equal N 1 = N 2 , these limits all lead to the same topology for the phase diagram and provide a consistent global understanding of the phases of the theory. When N 1 = N 2 , different limits lead to distinct topologies of the phase diagram. This necessarily implies nontrivial physics at some intermediate regimes of parameter space. In the large N 1,2 limit, we argue that the topological transitions are accounted for by a (non-supersymmetric) duality cascade as one varies the parameters of the theory.

show abstract

From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling

Cited by 56 publications

References 112 publications

Modified instanton sum in QCD and higher-groups

Modified instanton sum in QCD and higher-groups

Anomaly constraints on deconfinement and chiral phase transition

The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade

Contact Info

Product

Resources

About