SU(3) Deconfinement in (2+1)d from Twisted Boundary Conditions and Self-Duality

Abstract: We study the pure SU(3) gauge theory in 2+1 dimensions on the lattice using 't Hooft's twisted boundary conditions to force non-vanishing center flux through the finite volume. In this way we measure the free energy of spacelike center vortices as an order parameter for the deconfinement transition. The transition is of 2nd order in the universality class of the 2d 3-state Potts model, which is self-dual. This self-duality can be observed directly in the SU(3) gauge theory, and it can be exploited to extract critical couplings with high precision in rather small volumes. We furthermore obtain estimates for critical exponents and the critical temperature in units of the dimensionful continuum coupling. Finally, we also apply our methods to the (2+1)d SU(4) gauge theory which was previously found to have a weak 1st order transition. We nevertheless observe at least approximate q = 4 Potts scaling at length scales corresponding to the lattice sizes used in our simulations.