Rutgers University Department of Physics and Astronomy
Video File

Heeyeon Kim
(University of Oxford)

Supersymmetric partition functions, 't Hooft anomalies and Holomorphy

Supersymmetric partition functions on compact spaces provide an important tool to study the non-perturbative aspects of quantum field theories. In this talk, I discuss universal properties of the partition functions for 4d N=1 gauge theories. After reviewing the dependence of the partition function on various discrete and continuous parameters, I introduce a novel way to construct the partition function on a large class of four-manifolds which preserves two supersymmetries. In the second part of the talk, I discuss the existence of a mixed anomaly between supersymmetry and background gauge symmetry, which implies an anomaly in the holomorphy of the partition function with respect to the background gauge parameters. I propose a way to compute the full non-holomorphic dependence of the partition functions, which provides an important correction to earlier holomorphic results.

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