Witten deformation of Ray-Singer analytic torsion

Details Witten deformation of Ray-Singer analytic torsion Witten deformation of Ray-Singer analytic torsion

1994-08-16

arxiv.org/abs/dg-ga/9408002v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages. AMS-LaTeX

Scientific paper

Consider a flat vector bundle F over compact Riemannian manifold M and let f be a self-indexing Morse function on M. Let g be a smooth Euclidean metric on F. Set g_t=exp(-2tf)g and let \rho(t) be the Ray-Singer analytic torsion of F associated to the metric g_t. Assuming that the vector field $grad f$ satisfies the Morse-Smale transversality conditions, we provide an asymptotic expansion for log(\rho(t)) for t\to\infty of the form a_0+a_1t+b log(t)+o(1). We present explicit formulae for coefficients a_0,a_1 and b. In particular, we show that b is a half integer.

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