Localization for the norm-square of the moment map and the two-dimensional Yang-Mills integral

Details Localization for the norm-square of the moment map and the two-dimensional Yang-Mills integral Localization for the norm-square of the moment map and the two-dimensional Yang-Mills integral

2004-04-22

arxiv.org/abs/math/0404413v3

Mathematics

Symplectic Geometry

33 pages. Corrections and a few paragraphs re-written. To appear in Jour. Sympl. Geom

Scientific paper

The first seven sections of the paper contain a version of localization for the norm-square of the moment map in equivariant de Rham theory, similar to that proved by P.-E. Paradan. The last section contains a definition and computation of the Yang-Mills path integral in two dimensions. The idea is to reverse the logic in Witten's paper and take the localization formula as the definition of the path integral. Using a symmetry argument we show that the path integral is given by the Migdal formula.

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