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QCD at finite chemical potential in a small hyperspherical box
(University of Swansea, UK)
Auletta A1 (LNF)
We consider the phase diagram of QCD at finite chemical potential for low temperatures from one-loop perturbation theory on S^1 x S^3. Compactifying the spatial dimensions allows for calculation in the entire T-mu plane, for sufficiently small spatial volumes. The action of QCD is complex in the presence of a finite quark chemical potential, resulting in the sign problem. The consequence is that the gauge field configurations considered as a distribution must be complexified to give the dominant contributions to the path integral. For small enough N it is not necessary to consider a distribution and for N=3 we solve the integrals over the gauge fields numerically to obtain the occupation number, Polyakov loops, average phase, etc. For large N we must consider a distribution which is necessarily complex in order to use the saddle-point method to evaluate the gauge field integrals. This causes the eigenvalues of the Polyakov loop to move off the unit circle and onto a contour in the complex plane. In both cases we find an "atomic level" structure as a function of the chemical potential in that the occupation number, energy, and pressure increase in discrete steps. We show that each step corresponds to a 3rd order transition in the large N limit of the Gross-Witten type.