The Mathematics of Quantum Theory

A hyperholomorphic line bundle in ${\cal N}=2$ theories

25 May 2014, 14:45

45m

Alpha Gamma Rho Room (Buehler Alumni Center)

Speaker

Prof. Andy Neitzke (U. Texas)

Description

Compactifying ${\cal N}=2$ supersymmetric field theory from four to three dimensions on a circle gives rise to a complex integrable system carrying a hyperkahler metric. In many cases this integrable system carries in addition a canonical hyperholomorphic line bundle, conjecturally related to the physics of the theory compactified on Taub-NUT space. I will describe the construction of this line bundle, its connection to complex Chern-Simons theory, and a closely related new smooth generating function for BPS state counts / Donaldson-Thomas invariants. The bundle in some cases coincides with one introduced by Haydys and Alexandrov-Persson-Pioline.