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Research Van Swinderen Institute

VSI seminar Fabrizio Nieri

When:Th 09-05-2019 12:30 - 14:00
Where:FSE-Building 5111.0135

"Supersymmetric localization of 4d N=1 theories on D2xT2"

Since the pioneering work of Pestun, localization techniques have been successfully applied to computing protected observables in theories with varying amounts of supersymmetry and in diverse dimensions and backgrounds. 

For theories with N=1 supersymmetry in four dimensions, most of the studies have focused on closed compact spaces, while only few results for manifolds with boundaries are available, mostly in two and three dimensions. The formulation of supersymmetric theories on manifolds with boundaries is more fundamental to a large extent.

Indeed, the majority of the compact space results can be obtained from "half-spaces" through certain sewing procedures. Besides, the presence of boundaries is also interesting for studying aspects which would otherwise be lost, such as the physics of boundary conditions, interfaces and bulk/boundary coupled systems.

In this talk, I will consider 4d N=1 theories on a 2-disk times a 2-torus, and show how it is possible to compute the exact partition function through localization provided that certain boundary conditions are imposed. If time permits, I will also discuss particular 3d N=1 theories on the boundary 3-torus performing a ``flipping” between different boundary conditions.