Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres

Details Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres

2010-12-11

arxiv.org/abs/1012.2414v1

Communications in Mathematical Physics 311 (2012) 713-753

Physics

High Energy Physics

High Energy Physics - Theory

40 pages

Scientific paper

10.1007/s00220-012-1418-y

We study the covariantly constant Savvidy-type chromomagnetic vacuum in finite-temperature Yang-Mills theory on the four-dimensional curved spacetime. Motivated by the fact that a positive spatial curvature acts as an effective gluon mass we consider the compact Euclidean spacetime $S^1\times S^1\times S^2$, with the radius of the first circle determined by the temperature $a_1=(2\pi T)^{-1}$. We show that covariantly constant Yang-Mills fields on $S^2$ cannot be arbitrary but are rather a collection of monopole-antimonopole pairs. We compute the heat kernels of all relevant operators exactly and show that the gluon operator on such a background has negative modes for any compact semi-simple gauge group. We compute the infrared regularized effective action and apply the result for the computation of the entropy and the heat capacity of the quark-gluon gas. We compute the heat capacity for the gauge group SU(2N) for a field configuration of $N$ monopole-antimonopole pairs. We show that in the high-temperature limit the heat capacity is well defined in the infrared limit and exhibits a typical behavior of second-order phase transition $\sim (T-T_c)^{-3/2}$ with the critical temperature $T_c=(2\pi a)^{-1}$, where $a$ is the radius of the 2-sphere $S^2$.

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