Field theory in the 1/2 Omega-background

          @misc{ scivideos_PIRSA:22060087,
            doi = {10.48660/22060087},
            url = {https://pirsa.org/22060087},
            author = {Hollands, Lotte},
            keywords = {Mathematical physics},
            language = {en},
            title = {Field theory in the 1/2 Omega-background},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060087 see, \url{https://scivideos.org/pirsa/22060087}}
          }
          

Abstract

In this lecture I'll discuss various aspects of 4d N=2 and 5d N=1 supersymmetric QFT's in the 1/2 Omega-background (and along the way try to emphasize some relations to the 3d N=2 theories discussed in this workshop). Central to this story is the Nekrasov instanton partition function (or topological string partition function) in this background, which we will obtain through abelianization as an integral of a ratio of Wronskians of certain special solutions to the relevant Schrodinger equation. We will argue that a slight generalization of the above partition function solves an associated Riemann-Hilbert problem and defines a section of a distinguished line bundle over the moduli space of flat connections.