BRST treatment of zero modes for the worldline formalism in curved space

Details BRST treatment of zero modes for the worldline formalism in curved space BRST treatment of zero modes for the worldline formalism in curved space

2003-12-05

arxiv.org/abs/hep-th/0312064v2

JHEP 0401 (2004) 023

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, no figures; misprints corrected

Scientific paper

10.1088/1126-6708/2004/01/023

One-loop quantities in QFT can be computed in an efficient way using the worldline formalism. The latter rests on the ability of calculating 1D path integrals on the circle. In this paper we give a systematic discussion for treating zero modes on the circle of 1D path integrals for both bosonic and supersymmetric nonlinear sigma models, following an approach originally introduced by Friedan. We use BRST techniques and place a special emphasis on the issue of reparametrization invariance. Various examples are extensively analyzed to verify and test the general set-up. In particular, we explicitly check that the chiral anomaly, which can be obtained by the semiclassical approximation of a supersymmetric 1D path integral, does not receive higher order worldline contributions, as implied by supersymmetry.

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