Higher length-twist coordinates and applications - effective superpotentials from the geometry of opers

          @misc{ scivideos_PIRSA:18080058,
            doi = {10.48660/18080058},
            url = {https://pirsa.org/18080058},
            author = {Kidawi, Omar},
            keywords = {Mathematical physics},
            language = {en},
            title = {Higher length-twist coordinates and applications - effective superpotentials from the geometry of opers},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2018},
            month = {aug},
            note = {PIRSA:18080058 see, \url{https://scivideos.org/pirsa/18080058}}
          }
          

Abstract

We describe joint work with L. Hollands on the geometry of the moduli space of flat connections over a Riemann surface. On the one hand, we generalize and compute certain "complexified Fenchel-Nielsen" coordinates for SL(2)-connections to higher rank using the spectral network "abelianization" approach of Gaiotto-Moore-Neitzke. We then use these coordinates to compute superpotentials, following a conjecture of Nekrasov-Rosly-Shatashvili which roughly states the following: a certain low energy effective twisted superpotential arising from compactifying a theory of class S is equal to the generating function (in the sense of symplectic geometry), in some special coordinates, of the Lagrangian submanifold of opers in the associated moduli space of flat connections.