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

Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other compatible player.

Speaker(s):

Scientific Areas:

Collection/Series:

PIRSA Number:

18080058

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.

©2012 Perimeter Institute for Theoretical Physics