Novel first-order phase transition and critical points on Yang-Mills theory in

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

We examine the thermal properties and phase transitions of Yang-Mills theory formulated on the spacetime manifold , where two spatial directions are compactified. Using both lattice simulations and an effective model, we study the theory in Euclidean space with anisotropic spatial volumes. Our lattice analysis reveals that significant pressure anisotropy appears only when the compactified spatial dimensions are sufficiently short, in contrast to free scalar theories. Based on these results, we construct an effective theory where two Polyakov loops associated with the compactified directions are treated as dynamical degrees of freedom. This model, tuned to match the lattice thermodynamics, predicts a novel first-order phase transition terminating at critical points. Our findings suggest that the coupling between the two Polyakov loops plays a key role in driving this transition.