The Yang-Mills Gradient Flow and Loop Spaces of Compact Lie Groups

Details The Yang-Mills Gradient Flow and Loop Spaces of Compact Lie Groups The Yang-Mills Gradient Flow and Loop Spaces of Compact Lie Groups

2011-04-28

arxiv.org/abs/1104.5514v2

Mathematics

Differential Geometry

52 pages

Scientific paper

We study the L^2 Yang-Mills gradient flow as a Morse function on the space of connection 1-forms on a principal G-bundle P$ over the sphere S^2. The resulting Morse homology is compared to the heat flow homology of the space of based loops in the compact Lie group G. An isomorphism between these two Morse homologies is obtained by coupling a perturbed version of the Yang-Mills gradient flow with the L^2 gradient flow of the classical action functional on loops. Our result gives an affirmative answer to a query by Atiyah.

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