5. Theoretical Physics (CSN4)

QCD at finite chemical potential in a small hyperspherical box

by Joyce Myers (University of Swansea, UK)

Auletta A1 (LNF)

Auletta A1


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.
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