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


The bibtex entry for the article can be downloaded here.


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.