SUPERSYMMETRIC PARTICLE IN A SPACETIME WITH TORSION AND THE INDEX THEOREM - ART. NO. 045014

The supersymmetric Lagrangian compatible with the presence of torsion in the background spacetime requires, in addition to the minimal coupl ing, an interaction between the spin and the torsion of the form 1/2N (mu nu lambda rho) psi(mu)psi(nu)psi(lambda)psi(rho), where N is the N ieh-Yan 4-form. This gives rise to a coupling between helicity (h) and the Nieh-Yan density of the form hN. The classical Lagrangian allows computing the index for the Dirac operator on a four-dimensional compa ct manifold with curvature and torsion using the path integral represe ntation for the index. This calculation provides an independent check for the recent result of the chiral anomaly in spaces with torsion.