Field theory in the 1/2 Omega-background


Hollands, L. (2022). Field theory in the 1/2 Omega-background. Perimeter Institute. https://pirsa.org/22060087


Hollands, Lotte. Field theory in the 1/2 Omega-background. Perimeter Institute, Jun. 29, 2022, https://pirsa.org/22060087


          @misc{ pirsa_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},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060087 see, \url{https://pirsa.org}}

Lotte Hollands Heriot-Watt University


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.