On The Phase Transition in D=3 Yang-Mills Chern-Simons Gauge Theory

Abstract

$SU(N)$ Yang-Mills theory in three dimensions, with a Chern-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 $k\gg N$, 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 non-perturbative 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 $k$, called $k_c$, with $k_c/N\approx 2\pm .7$. Three lines of evidence are given: First, a gauge-invariant one-loop calculation shows that the perturbative theory has tachyonic problems if $k\le 29N/12$.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 $k\le k_c$ there is a non-trivial vacuum condensate driven by soliton entropy and driving a gauge-boson dynamical mass $M$, while both the condensate and $M$ vanish for $k\ge k_c$. Third, we study possible quantum solitons stemming from an effective action having both a Chern-Simons mass $m$ and a (gauge-invariant) dynamical mass $M$. We show that if $M \gsim 0.5 m$, 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 $M\to 0$.

36 pages, latex, two .eps and three .ps figures in a gzipped uuencoded file

References in corpus (3)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• String Tension and Chern-Simons Fluctuations in the Vortex Vacuum of d=3 Gauge Theory

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• Sphalerons, knots, and dynamical compactification in Yang-Mills-Chern-Simon theories
• Magnetic Symmetries and Vortices In Chern-Simons Theories
• On the deconfining limit in (2+1)-dimensional Yang-Mills theory
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