Pressure and phase structure in pure Yang-Mills theory on the anisotropic boundary condition

Fujii, Daisuke; Iwanaka, Akihiro*; Suenaga, Daiki*; Kitazawa, Masakiyo*

The Matsubara formalism for the thermal quantum field theory introduces temperature into the theory as a boundary condition along the imaginary time direction of Euclidean spacetime. In this study, we further consider the pure Yang-Mills theory on with boundary conditions in one spatial direction, and discuss thermodynamic quantities and their phase structures. The introducing of the boundary condition leads to the breaking of rotational symmetry, which results in anisotropy of the pressure. Results from lattice QCD simulations show that the anisotropic effect is suppressed until the spatial spread becomes significantly smaller near the critical temperature. This result is a very different behavior from that of free-particle systems. In order to reveal the mechanism behind this result, we employ an effective model with two Polyakov loops along the time and spatial directions. We show that introducing the competition between the two Polyakov loops as suggested in a previous study describes well the lattice data in the high temperature region. Furthermore, we show that a new first-order phase transition is suggested, which is different from the confinement phase transition.