Stability conditions and the Painleve equations

Mr Tom Sutherland (University of Oxford)

Friday 4th November, 2011 16:00-17:00 204


I will describe the space of Bridgeland stability conditions of the category of B-branes of certain $d=4, N=2$ field theories appearing in a paper of Gaiotto, Moore and Neitzke (arXiv:0907.3987). We give a biholomorphism from the universal cover of moduli the space of elliptic curves to the space of stability conditions which lifts the period map of a meromorphic differential on a 1-dimensional family of elliptic curves.

We can interpret this family of elliptic curves as the total space of Hitchin's fibration on the moduli space of flat connections on the projective line with certain prescribed poles of a given multiplicity. This moduli space is the space of initial conditions for one of the Painleve equations which describe isomonodromic deformations of these connections.

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