PIRSA:18080058 Conference Mathematical physics

DOI10.48660/18080058

Conference/School: Higher Algebra and Mathematical Physics

Kidawi, O. (2018). Higher length-twist coordinates and applications - effective superpotentials from the geometry of opers. Perimeter Institute. https://pirsa.org/18080058

Kidawi, Omar. Higher length-twist coordinates and applications - effective superpotentials from the geometry of opers. Perimeter Institute, Aug. 16, 2018, https://pirsa.org/18080058 

@misc{ pirsa_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},
  year = {2018},
  month = {aug},
  note = {PIRSA:18080058 see, \url{https://pirsa.org}}
}

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.

Resources

Next talk

Related Talks