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Instanton Counting, Matrix Models, And Characters, Spencer Tamagni

Honors Undergraduate Theses

In this thesis we study symmetries of quantum field theory visible only at the non-perturbative level, which arise from large deformations of the integration contour in the path integral. We exposit the recently-developed theory of qq-characters that organizes such symmetries in the case of N = 2 supersymmetric gauge theories in four dimensions. We sketch the physical origin of such observables from intersecting branes in string theory, and the mathematical origin as certain
equivariant integrals over Nakajima quiver varieties. We explain some of the main applications, including the derivation of Seiberg-Witten geometry for quiver gauge theories and the relations to …