Phase transition in D=3 Yang-Mills Chern-Simons gauge theory

SU(N) Yang-Mills theory in three dimensions, with a Chem-Simons term of level k (an integer) added, has two-dimensionful coupling constants g(2)k and g(2)N; its possible phases depend on the size of k relative to N. For k much greater than N, this theory approaches topological Chern-Simons theory with no Yang-Mills term, and expectation values of multiple Wilson loops yield Jones polynomials, as Witten has shown; it can be treated semiclassically. For k=0, the theory is badly infrared singular in perturbation theory, a nonperturbative mass and subsequent quantum solitons are generated, and Wilson loops show an area law. We argue that there is a phase transition between these two behaviors at a critical value of k(c) called k(c), with k(c)/N approximate to 2+/-0.7. Three lines of evidence are given. First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if k less than or equal to 29N/12. The theory becomes sensible only if there is an additional dynamic source of gauge-boson mass, just as in the k=0 case. Second, we study in a rough approximation the free energy and show that for k less than or equal to k(c) then is a nontrivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass M, while both the condensate and M vanish for k greater than or equal to k(c). Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass m and a (gauge-invariant) dynamical mass Arl. We show that if M greater than or similar to 0.5m, there are finite-action quantum sphalerons, while none survive in the classical limit M=0, as shown earlier by D'Hoker and Vinet. There are also quantum topological vortices smoothly vanishing as M-->0.