Higher length-twist coordinates and applications - effective superpotentials from the geometry of opers
APA
Kidawi, O. (2018). Higher length-twist coordinates and applications - effective superpotentials from the geometry of opers. Perimeter Institute. https://pirsa.org/18080058
MLA
Kidawi, Omar. Higher length-twist coordinates and applications - effective superpotentials from the geometry of opers. Perimeter Institute, Aug. 16, 2018, https://pirsa.org/18080058
BibTex
@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}} }
University of Toronto
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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.