Heat Kernel and Moduli Space
Copyright policy )Heat Kernel and Moduli Space
The author describes a proof of the formulas of \textit{E. Witten} [Commun. Math. Phys. 141, No. 1, 153-209 (1991; Zbl 0762.53063); J. Geom. Phys. 9, No. 4, 303-368 (1992; Zbl 0768.53042)] about the symplectic volumes and the intersection numbers of the moduli spaces of principal bundles on a compact Riemann surface. It is known that these formulas give all the information needed for the Verlinde formula. The main idea of the proof is to use the heat kernel on compact Lie groups, in a way very similar to the heat kernel proof of the Atiyah-Singer index formula and the Atiyah-Bott fixed point formula. The Reidemeister torsion comes into the picture, through a beautiful observation of Witten, as the symplectic volume of the moduli space. It plays the role similar to that played by the Ray-Singer torsion in the path-integral computations on the space of connections.
- Stanford University United States
principal bundles, symplectic volumes, compact Riemann surface, Moduli problems for differential geometric structures, moduli spaces, heat kernel on compact Lie groups, intersection numbers, heat equation method, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Yang-Mills and other gauge theories in quantum field theory
principal bundles, symplectic volumes, compact Riemann surface, Moduli problems for differential geometric structures, moduli spaces, heat kernel on compact Lie groups, intersection numbers, heat equation method, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Yang-Mills and other gauge theories in quantum field theory
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