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

^* e-mail: daiki.suenaga@riken.jp
^** e-mail: kitazawa@yukawa.kyoto-u.ac.jp

Published online: 22 December 2022

Abstract

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.