Strong coupling phase in lattice gauge theories at large dimension

Abstract

We study lattice gauge theories at large space-time dimension D. In the strong coupling (high-temperature) phase, the appropriate expansion parameter is D − 1 4 . We find that this phase, which becomes metastable at a certain temperature, is limited by a singular point which looks like a second-order phase transition. For the Z 2 gauge group, this happens at D tanh 4β = 128 3125 . At this temperature, the correlation length of two plaquettes becomes infinite. At D = ∞, the same result holds for any gauge group, only the value at which the transition occurs depends on the group. The corrections of orders D − 1 4 are different for different gauge groups. It is not yet clear to us if the Wilson loop changes its behaviour when the plaquette-plaquette correlation function does.