Speaker
Description
4d N = 2 supersymmetric theories are known to be connected with differential equations. We study a specific example of SU(2) Nf = 1 theory which corresponds to a Schrodinger equation. An important quantity to study in the exact WKB analysis of the Schrodinger equation is the quantum period, also known as the Voros symbol, which is defined as the Borel summation of the term by term integration of the formal WKB series solving the Schrodinger equation. There are 3 other equivalent definitions of quantum periods, including the holonomy, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and using instanton counting. In particular, instanton counting provides an analytic solution to the TBA equation. Similarly 5d N=1 theories compactified on a circle are connected to difference equation. We study the 5d theory given by the resolved conifold and here open topological string partition functions provide resummations of the WKB series solving difference equation.
