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Arturo Prat-Waldron: On the Construction of the Dirac Operator

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Published on Jul 26, 2012

Arturo Prat-Waldron (Max-Planck-Institut fuer Mathematik, Bonn, Germany)
Complete Title: On the Construction of the Dirac Operator via Geometric Quantization of Supermanifolds

Abstract: In this talk we discuss the geometric quantization of a certain symplectic supermanifold obtained from considering a one-dimensional supersymmetric sigma model on a Riemannian manifold.

We study the relation between the metaplectic correction in the super-setting and spin structures and we construct the heat kernel of the Dirac operator of a spin manifold by quantizing an appropriate symmetry of the system using a supersymmetric version of the Blattner-Kostant-Sternberg pairing.

We explain how this point of view fits into the Stolz-Teichner program of studying cohomology theories via super-symmetric field theories.

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