Effective Action and Phase Transitions in Yang-Mills Theory on Spheres |
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Authors: | Email author" target="_blank">Ivan?G?AvramidiEmail author Samuel?Collopy |
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Institution: | 1.Department of Mathematics,New Mexico Institute of Mining and Technology,Socorro,USA |
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Abstract: | 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 × S
1 × S
2, with the radius of the first circle determined by the temperature a
1 = (2π
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 per unit volume is well defined
in the infrared limit and exhibits a typical behavior of second-order phase transition ~ (T-Tc)-3/2{\sim(T-T_c)^{-3/2}} with the critical temperature T
c
= (2π
a)−1, where a is the radius of the 2-sphere S
2. |
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Keywords: | |
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