At large Im tau the superconformal index tends to 1, and the authors show that a Picard-Lefschetz analysis of a Lorentzian-inspired bulk integral enforces this by making all exponentially large black hole saddles irrelevant via Stokes phenomena.
The Mathai-Quillen Formalism and Topological Field Theory
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abstract
These lecture notes give an introductory account of an approach to cohomological field theory due to Atiyah and Jeffrey which is based on the construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics covered are: an explanation of the Mathai-Quillen formalism for finite dimensional vector bundles; the definition of regularized Euler numbers of infinite dimensional vector bundles; interpretation of supersymmetric quantum mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over spaces of connections.
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Superconformal indices and black hole saddles
At large Im tau the superconformal index tends to 1, and the authors show that a Picard-Lefschetz analysis of a Lorentzian-inspired bulk integral enforces this by making all exponentially large black hole saddles irrelevant via Stokes phenomena.