Abstract
The dynamics of zero modes in gauge theory is highly nontrivial due to its nonperturbative nature even in the case where the other modes can be treated perturbatively. One of the related issues concerns the possible instability of the trivial vacuum Aμ(x) = 0 due to the existence of nontrivial degenerate vacua known as “torons”. Here we investigate this issue for the 4D SU(2) and SU(3) pure Yang-Mills theories on the lattice by explicit Monte Carlo calculation of the Wilson loops and the Polyakov line at large β. While we confirm the leading 1/β predictions obtained around the trivial vacuum in both SU(2) and SU(3) cases, we find that the subleading term vanishes only logarithmically in the SU(2) case unlike the power-law decay in the SU(3) case. In fact, the 4D SU(2) case is marginal according to the criterion by Coste et al. Here we show that the trivial vacuum dominates in this case due to large fluctuations of the zero modes around it, thereby providing a clear understanding of the observed behaviors.
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References
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, The Twisted Eguchi-Kawai Model: A Reduced Model for Large N Lattice Gauge Theory, Phys. Rev. D 27 (1983) 2397 [INSPIRE].
A. Gonzalez-Arroyo and M. Okawa, Large N reduction with the Twisted Eguchi-Kawai model, JHEP 07 (2010) 043 [arXiv:1005.1981] [INSPIRE].
N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [INSPIRE].
K.N. Anagnostopoulos et al., Progress in the numerical studies of the type IIB matrix model, arXiv:2210.17537 [https://doi.org/10.1140/epjs/s11734-023-00849-x] [INSPIRE].
A. Coste, A. Gonzalez-Arroyo, J. Jurkiewicz and C.P. Korthals Altes, Zero Momentum Contribution to Wilson Loops in Periodic Boxes, Nucl. Phys. B 262 (1985) 67 [INSPIRE].
Z. Fodor et al., The Yang-Mills gradient flow in finite volume, JHEP 11 (2012) 007 [arXiv:1208.1051] [INSPIRE].
Z. Fodor et al., The gradient flow running coupling scheme, PoS LATTICE2012 (2012) 050 [arXiv:1211.3247] [INSPIRE].
W. Krauth and M. Staudacher, Eigenvalue distributions in Yang-Mills integrals, Phys. Lett. B 453 (1999) 253 [hep-th/9902113] [INSPIRE].
T. Yokota et al., Color superconductivity on the lattice — analytic predictions from QCD in a small box, JHEP 06 (2023) 061 [arXiv:2302.11273] [INSPIRE].
S. Hands, T.J. Hollowood and J.C. Myers, Numerical Study of the Two Color Attoworld, JHEP 12 (2010) 057 [arXiv:1010.0790] [INSPIRE].
S. Ueda et al., Development of an object oriented lattice QCD code ‘Bridge++’, J. Phys. Conf. Ser. 523 (2014) 012046 [INSPIRE].
Y. Akahoshi et al., General purpose lattice QCD code set Bridge++ 2.0 for high performance computing, J. Phys. Conf. Ser. 2207 (2022) 012053 [arXiv:2111.04457] [INSPIRE].
Acknowledgments
We would like to thank Etsuko Itou for providing us with some results in 4D SU(2) gauge theory at finite density. We are also grateful to Yuta Ito, Hideo Matsufuru, Yusuke Namekawa, Asato Tsuchiya, Shoichiro Tsutsui and Takeru Yokota for discussions on finite density QCD, which motivated the present work. The computations were carried out on the PC clusters in KEK Computing Research Center and KEK Theory Center. We have used Bridge++ (http://bridge.kek.jp/Lattice-code/), which is a code set for numerical simulations of lattice gauge theories based on C++ [12, 13]. We would like to thank Hideo Matsufuru for his help concerning the usage of this code set.
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Asano, Y., Nishimura, J. The dynamics of zero modes in lattice gauge theory — difference between SU(2) and SU(3) in 4D. J. High Energ. Phys. 2023, 204 (2023). https://doi.org/10.1007/JHEP11(2023)204
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DOI: https://doi.org/10.1007/JHEP11(2023)204