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Omar Kidwai (Toronto)
February 22 @ 3:00 pm - 4:00 pm UTC+0
Higher length-twist coordinates for character varieties.
We describe joint work with L. Hollands on a construction of special holomorphic Darboux coordinates on certain SL_N (particularly N=2,3) character varieties. We consider degenerate examples of “spectral networks” of Gaiotto-Moore-Neitzke (certain graphical objects on a Riemann surface), generalizing the so-called “Fenchel-Nielsen” networks of Hollands-Neitzke. We compute the associated “spectral coordinates” using the “abelianization map”, taking connections on the Riemann surface to abelian holonomy data on a spectral cover, generalizing the “complexified Fenchel-Nielsen” coordinates of Kourouniotis-Tan for SL(2)-connections to higher rank. Time permitting, I will discuss some physical applications to computing superpotentials coming from 4d N=2 supersymmetric QFTs.