SINGULARITY-THEORY AND N=2 SUPERSYMMETRY

Author:

CECOTTI S.1,GIRARDELLO L.2,PASQUINUCCI A.3

Affiliation:

1. International School for Advanced Studies, SISSA—ISAS, Trieste and I.N.F.N., sez. di Trieste, Trieste, Italy

2. Dipartimento di Fisica, Universitá di Milano, and I.N.F.N., sez. di Milano, Milano, Italy

3. International School for Advanced Studies, SISSA-ISAS, Trieste and I.N.F.N., sez. di Trieste, Trieste, Italy

Abstract

N=2 supersymmetry in two dimensions can be seen as a quantum realization of the geometry of singularity theory. We show this using non-perturbative methods. N=2 susy is related to the Picard-Lefschetz theory much in the same way as N=1 susy is related to Morse theory. All the concepts of singularity theory fit in the physics of the N=2 Landau-Ginsburg models. The critical behaviour of the theory is encoded in a certain natural “gauge-connection” in coupling-constant space. It is flat for a quashihomogeneous superpotential, but not in general. We find an explicit formula relating it to the Gauss-Manin connection of the singularity associated to the superpotential. Our results are valid for both the quasihomogeneous and the non-quasihomogeneous case, but in the former our equations simplify dramatically. We discuss some preliminary applications.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

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