On the Coleman-Hill Theorem

Details On the Coleman-Hill Theorem On the Coleman-Hill Theorem

1994-08-16

arxiv.org/abs/hep-th/9408091v1

Phys.Lett. B343 (1995) 239-243

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, REVTEX, UdeM-GPP-TH-94-5

Scientific paper

10.1016/0370-2693(94)01420-H

The Coleman-Hill theorem prohibits the appearance of radiative corrections to the topological mass (more precisely, to the parity-odd part of the vacuum polarization tensor at zero momentum) in a wide class of abelian gauge theories in 2+1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum polarization tensor. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Simons electrodynamics, obeys the new non-renormalization theorem. Whereas the vacuum polarization {\sl does} receive a one-loop, parity-odd correction, this does not translate to a radiative contribution to the Chern-Simons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooked in the original analysis, where the conditions of the theorem are satisfied and where the topological mass does, in fact, get a radiative correction.

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