Abstract
It has recently been shown that a center-twisted compactification of the four-dimensional pure SU(N) Yang-Mills theory on a three-torus gives rise to the twodimensional ℂℙN− 1-model on a circle with a flavor-twisted boundary condition. We verify the consistency of this statement non-perturbatively at theta angle θ = π, in terms of the mixed ’t Hooft anomalies for flavor symmetries and the time-reversal symmetry. This provides further support for the approach to the confinement of four-dimensional Yang-Mills theory from the two-dimensional ℂℙN− 1-model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Eichenherr, SU(N) Invariant Nonlinear σ-models, Nucl. Phys. B 146 (1978) 215 [Erratum ibid. B 155 (1979) 544] [INSPIRE].
V.L. Golo and A.M. Perelomov, Solution of the Duality Equations for the Two-Dimensional SU(N) Invariant Chiral Model, Phys. Lett. B 79 (1978) 112 [INSPIRE].
E. Cremmer and J. Scherk, The Supersymmetric Nonlinear σ-model in Four-Dimensions and Its Coupling to Supergravity, Phys. Lett. B 74 (1978) 341 [INSPIRE].
S. Cecotti and C. Vafa, On classification of N = 2 supersymmetric theories, Commun. Math. Phys. 158 (1993) 569 [hep-th/9211097] [INSPIRE].
S. Cecotti and C. Vafa, Exact results for supersymmetric σ-models, Phys. Rev. Lett. 68 (1992) 903 [hep-th/9111016] [INSPIRE].
N. Dorey, The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms, JHEP 11 (1998) 005 [hep-th/9806056] [INSPIRE].
N. Dorey, T.J. Hollowood and D. Tong, The BPS spectra of gauge theories in two-dimensions and four-dimensions, JHEP 05 (1999) 006 [hep-th/9902134] [INSPIRE].
M. Yamazaki and K. Yonekura, From 4d Yang-Mills to 2d ℂℙN− 1 model: IR problem and confinement at weak coupling, JHEP 07 (2017) 088 [arXiv:1704.05852] [INSPIRE].
G.V. Dunne and M. Ünsal, Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model, JHEP 11 (2012) 170 [arXiv:1210.2423] [INSPIRE].
A.D. Linde, Infrared Problem in Thermodynamics of the Yang-Mills Gas, Phys. Lett. B 96 (1980) 289 [INSPIRE].
J. Écalle, Les fonctions résurgentes, I-III, Publications Mathématiques d’Orsay, (1981).
T. Eguchi and H. Kawai, Reduction of Dynamical Degrees of Freedom in the Large N Gauge Theory, Phys. Rev. Lett. 48 (1982) 1063 [INSPIRE].
A. Gonzalez-Arroyo and M. Okawa, A Twisted Model for Large N Lattice Gauge Theory, Phys. Lett. B 120 (1983) 174 [INSPIRE].
A. Gonzalez-Arroyo and M. Okawa, The Twisted Eguchi-Kawai Model: A Reduced Model for Large N Lattice Gauge Theory, Phys. Rev. D 27 (1983) 2397 [INSPIRE].
M. Lüscher, A New Method to Compute the Spectrum of Low Lying States in Massless Asymptotically Free Field Theories, Phys. Lett. B 118 (1982) 391 [INSPIRE].
M. Lüscher and G. Munster, Weak Coupling Expansion of the Low Lying Energy Values in the SU(2) Gauge Theory on a Torus, Nucl. Phys. B 232 (1984) 445 [INSPIRE].
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, Time Reversal and Temperature, JHEP 05 (2017) 091 [arXiv:1703.00501] [INSPIRE].
Y. Tanizaki, T. Misumi and N. Sakai, Circle compactification and ’t Hooft anomaly, JHEP 12 (2017) 056 [arXiv:1710.08923] [INSPIRE].
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59 (1980) 135.
E. Looijenga, Root Systems and Elliptic Curves, Invent. Math. 38 (1977) 17.
E. Looijenga, Invariant Theory For Generalized Root Sytems, Invent. Math. 61 (1980) 1.
R. Friedman, J. Morgan and E. Witten, Vector bundles and F-theory, Commun. Math. Phys. 187 (1997) 679 [hep-th/9701162] [INSPIRE].
G. ’t Hooft, A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories, Nucl. Phys. B 153 (1979) 141 [INSPIRE].
E. Witten, Supersymmetric index in four-dimensional gauge theories, Adv. Theor. Math. Phys. 5 (2002) 841 [hep-th/0006010] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
Z. Komargodski, A. Sharon, R. Thorngren and X. Zhou, Comments on Abelian Higgs Models and Persistent Order, arXiv:1705.04786 [INSPIRE].
E. Witten, Large N Chiral Dynamics, Annals Phys. 128 (1980) 363 [INSPIRE].
E. Witten, Theta dependence in the large N limit of four-dimensional gauge theories, Phys. Rev. Lett. 81 (1998) 2862 [hep-th/9807109] [INSPIRE].
G.V. Dunne and M. Ünsal, Continuity and Resurgence: towards a continuum definition of the ℂℙ(N − 1) model, Phys. Rev. D 87 (2013) 025015 [arXiv:1210.3646] [INSPIRE].
Y. Nomura, T. Watari and M. Yamazaki, Pure Natural Inflation, Phys. Lett. B 776 (2018) 227 [arXiv:1706.08522] [INSPIRE].
Y. Nomura and M. Yamazaki, Tensor Modes in Pure Natural Inflation, Phys. Lett. B 780 (2018) 106 [arXiv:1711.10490] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1711.04360
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Yamazaki, M. Relating ’t Hooft anomalies of 4d pure Yang-Mills and 2d ℂℙN− 1 model. J. High Energ. Phys. 2018, 172 (2018). https://doi.org/10.1007/JHEP10(2018)172
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2018)172