Mathematics Colloquia and Seminars

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We will revisit the localization computation for the expectation values of 't Hooft operators in N=2 SU(N) theories with adjoint and fundamental matter on R^3 x S^1. We will show that the non-perturbative part of the answer arising from ''monopole bubbling" on R^3 is given by the Witten index of a certain supersymmetric quiver quantum mechanics, and discuss the precise map between the defect data and the quiver data. For N=2* theory, the Witten index formula reproduces the expressions obtained by Okuda, Ito and Taki (IOT). For SU(N) theory with N_f=2N flavors, the IOT expressions are known to differ from expressions computed using the AGT prescription. In the simplest example of an SU(2) theory with N_f=4 flavors, we will discuss how the aforementioned Witten index reproduces the AGT formula, after one takes into account the wall-crossing property of the index with respect to FI parameters in the supersymmetric quantum mechanics. This talk will be based on the paper 1801.01986, and work in progress with Daniel Brennan and Gregory Moore.