Prof. Dr. Gaetan Borot

Title: N = 2 supersymmetric gauge theories and topological recursion

Abstract:

I will report on recent progress with Bouchard, Chidambaram and Creutzig establishing that Whittaker vectors (also called Gaiotto vectors and representing instanton partition function on equivariant C^2) and the Nekrasov partition function (of instantons on equivariant P^2) for N = 2 supersymmetric gauge theory with gauge group SU(n) can be computed by the topological recursion. The starting point is a form of the Alday-Gaiotto-Tachikawa conjecture established by Schiffman-Vasserot and Braverman-Nakajima-Finkelberg and stating that the cohomology of a suitable compactification of the moduli space of G-bundles on P^2 carries an action of the W(gl_r) algebra and the fundamental class is a Whittaker vector for this action. Our approach suggests a route to prove rigorously that the all-order \hbar = -\epsilon_1\epsilon_2 expansion of the Whittaker vector partition function can be extracted (by means of the topological recursion) from a curve related to (but different from) the Seiberg-Witten curve.