A gauge invariant action for (2 + 1)-dimensional topologically massive Yang-Mills theory

✍ Scribed by Daniel Gonzales; A.N Redlich

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 682 KB
• Volume: 169
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(86)90160-0

✦ Synopsis

Under homotopically non-trivial gauge transformations, ci,,, with winding number n, the action, I, for topologically massive Yang-Mills theory changes by 2nn: I-+ I + 2nn. Equivalently, Gauss' law requires the physical states vl,,,[A] to change by a phase under time-independent gauge transformations: A"= UtAU+ UfdU, Y,,,[AU]=exp[-ia(A, U)] Y,,,[A]. By a unitary transformation, Y'[A] = e iw[alYIA],

we remove this phase (the Gauss law condition becomes the usual Y$,,[A'] = vlb,,[A]) and find a new action, I', which is manifestly gauge invariant, but is spatially non-local and not manifestly Lorentz invariant. W[A] is proportional to the one-loop chiral fermion effective action, -i In det(8 + A) in two dimensions. In the primed system, analysis of the wavefunctional !P& [A] near points in gauge function space where the two-dimensional chiral determinant, det(A + A), vanishes leads to quantization of the mass parameter p. We use our results to comment upon the connection between the (2n + I)-dimensional non-perturbative anomaly and anomalies in one higher and one lower dimension. Cl 1986 Academic Press, Inc