Phase transition in {ital D}=3 Yang-Mills Chern-Simons gauge theory
- Physics Department, University of California at Los Angeles, 405 S. Hilgard Ave., Los Angeles, California 90095-1547 (United States)
SU({ital N}) Yang-Mills theory in three dimensions, with a Chern-Simons term of level {ital k} (an integer) added, has two-dimensionful coupling constants {ital g}{sup 2}{ital k} and {ital g}{sup 2}{ital N}; its possible phases depend on the size of {ital k} relative to {ital N}. For {ital k}{gt}{ital 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 {ital 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 {ital k}, called {ital k}{sub {ital c}}, with {ital k}{sub {ital c}}/{ital N}{approx_equal}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 {ital k}{le}29{ital N}/12. The theory becomes sensible only if there is an additional dynamic source of gauge-boson mass, just as in the {ital k}=0 case. Second, we study in a rough approximation the free energy and show that for {ital k}{le}{ital k}{sub {ital c}} there is a nontrivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass {ital M}, while both the condensate and {ital M} vanish for {ital k}{ge}{ital k}{sub {ital c}}. Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass {ital m} and a (gauge-invariant) dynamical mass {ital M}. We show that if {ital M}{approx_gt}0.5{ital m}, there are finite-action quantum sphalerons, while none survive in the classical limit {ital M}=0, as shown earlier by D`Hoker and Vinet. There are also quantum topological vortices smoothly vanishing as {ital M}{r_arrow}0. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 288882
- Journal Information:
- Physical Review, D, Vol. 54, Issue 2; Other Information: PBD: Jul 1996
- Country of Publication:
- United States
- Language:
- English
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