Geometry and Physics seminar @ IGAP

[Emanuele Tuillier Illingworth]

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***** Geometry and Physics seminar @ IGAP *****
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When: Tuesday March 26 at 14.30

Where: IGAP Seminar room ("new SISSA building" in via Beirut, II floor)

Speaker: Fabrizio Del Monte (SISSA)

Title: Class S Theories, Free Fermions and Isomonodromic Deformations 
Beyond Genus Zero

Abstract:
Using arguments from Conformal Field Theory, Gamayun Iorgov and Lisovyy 
provided in 2012 an explicit expression for the tau function of the 
sixth Painlevé equation as a Fourier transform of Virasoro conformal 
blocks. This "Kiev formula" has been later generalized to more general 
isomonodromic problems on the sphere, with both regular and irregular 
punctures. Further, by using the AGT correspondence, one can see that 
the isomonodromic tau function is the dual partition function of an 
appropriate class S theory, for which the Painlevé equations (and 
generalizations thereof) can be thought of as renormalization group or, 
for the conformal case, conformal manifold deformation equations.

In this talk we will first recap the role of Hitchin systems in the 
context of class S theories, and what the isomonodromy deformations mean 
from this perspective. Then, we will show how one can generalize the 
connection between gauge theory and isomonodromic deformations to the 
genus one case, by using an approach based on free fermions. This will 
provide a formula connecting the tau function to the dual partition 
function of a circular quiver gauge theory with both bifundamental and 
adjoint hypermultiplets, which has new features absent in the genus zero 
case._______________________________________________
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