Supersymmetric particle in a spacetime with torsion and the index theorem

Osvaldo Chandía, Jorge Zanelli

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The supersymmetric Lagrangian compatible with the presence of torsion in the background spacetime requires, in addition to the minimal coupling, an interaction between the spin and the torsion of the form 1/2Nμνλρψμψ νψλψρ, where N is the Nieh-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 compact manifold with curvature and torsion using the path integral representation for the index. This calculation provides an independent check for the recent result of the chiral anomaly in spaces with torsion.

Original languageEnglish
Article number045014
Pages (from-to)450141-450144
Number of pages4
JournalPhysical Review D
Issue number4
StatePublished - 15 Aug 1998
Externally publishedYes


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