# Mode Regularization for $$N=1,2$$ SUSY Sigma Model

### J. High Energy Phys. 10 (2008) 019

The full published version is available at IOPscience.

### arXiv 0807.2276

The preprint in pdf is available at arXiv.org.

### Bibtex

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 regu- larization: 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 world- line 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.