EPJ Web Conf.
Volume 274, 2022XVth Quark Confinement and the Hadron Spectrum Conference (ConfXV)
|Number of page(s)||8|
|Section||2 - Parallel Track A|
|Published online||22 December 2022|
Roles of Polyakov loops in Yang-Mills theory on 𝕋2 × ℝ2
1 Strangeness Nuclear Physics Laboratory, RIKEN Nishina Center, Wako 351-0198, Japan
2 Research Center for Nuclear Physics, Osaka University, Ibaraki 567-0048, Japan
3 Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502 Japan
4 J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK, 319-1106 Japan
5 Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043 Japan
Published online: 22 December 2022
We present an effective model of SU(N) pure Yang-Mills theory on 𝕋2 × ℝ2, where two directions are compactified with periodic boundary conditions. Our model includes two Polyakov loops serving as the order parameters of two center symmetries. Based on the model, for N = 2 and N = 3 we show that a rich phase diagram in terms of the center symmetries on 𝕋2 × ℝ2 is obtained. Besides, we demonstrate roles of the Polyakov loops by comparing with the recent lattice results focusing on thermodynamic quantities on 𝕋2 × ℝ2. We expect that analysis on 𝕋2 × ℝ2 provides us with a new clue toward further understanding of pure YM theory with the Polyakov loop at finite temperature.
© The Authors, published by EDP Sciences, 2022
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