English

Mode Regularization for N=1,2 SUSY Sigma Model

High Energy Physics - Theory 2012-09-24 v2

Abstract

Worldline N=1 and N=2 supersymmetric sigma models in curved background are useful to describe spin one-half and spin one particles coupled to external gravity, respectively. It is well known that worldline path integrals in curved space require regularization: we present here the mode-regularization for these models, finding in particular the corresponding counterterms, both in the case of flat and curved indices for worldline fermions. For N=1, using curved indices we find a contribution to the counterterm from the fermions that cancels the contribution of the bosons, leading to a vanishing total counterterm and thus preserving the covariance and supersymmetry of the classical action. Conversely in the case of N=2 supersymmetries we obtain a non-covariant counterterm with both curved and flat indices. This work completes the analysis of the known regularization schemes for N=1,2 nonlinear sigma models in one dimension.

Keywords

Cite

@article{arxiv.0807.2276,
  title  = {Mode Regularization for N=1,2 SUSY Sigma Model},
  author = {Roberto Bonezzi and Marco Falconi},
  journal= {arXiv preprint arXiv:0807.2276},
  year   = {2012}
}

Comments

15 pages

R2 v1 2026-06-21T11:00:30.046Z