Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-06-13
Int.J.Mod.Phys. A14 (1999) 463-480
Physics
High Energy Physics
High Energy Physics - Theory
17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty (available from LANL). Latex thrice
Scientific paper
10.1142/S0217751X99000233
We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter ($\alpha$) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon _{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$ is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously since the system is three dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this $\alpha$ dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.
Dilkes F. A.
Martin Christopher L.
McKeon Dennis G. C.
Sherry T. N.
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