Nuclear Physics & RIKEN Theory Seminar

We consider the phase diagram of QCD formulated in small spatial volumes. The benefit of the small spatial volume is that it allows for a perturbative calculation of the phase diagram which is valid for all temperatures and densities. The action of QCD is complex when the quarks are coupled to a non-zero chemical potential. This results in the sign problem which prevents lattice simulations using conventional techniques. From one-loop perturbation theory on S^1 x S^3 we calculate the phase diagram analytically in the T − mu plane in the large N and Nf limit by generalizing large N matrix model techniques for the case of a complex action. We compare with low temperature results for N = 3 obtained by performing the integrals over the gauge fields numerically. We calculate expectation values for several observables including the fermion number and the Polyakov lines. For the fermion number a Landau-level-like structure is observed as a function of the chemical potential and each level transition coincides with a spike in the Polyakov lines, indicating partial-filling of the level. In the large N limit each level transition corresponds to discontinuities in the fermion number which result in third-order transitions of the Gross-Witten-Wadia type. We confirm the appearance of the level-structure at low temperatures in lattice simulations of 2-color QCD where the sign problem is absent.