Fabrizio Del Monte, SISSA, Italie

Isomonodromic Conformal Field Theory on the Torus

Abstract: In the last few years, following the original spirit of the works on Holonomic Quantum Fields by Jimbo, Miwa and Sato, a new approach for the solution of a Riemann-Hilbert problem and its isomonodromic deformations has been proposed by Lisovyy et al, employing tools from two dimensional Conformal Field Theory and results from localization computation of partition functions in the context of supersymmetric gauge theories. In this talk the extension of these results to the case of the torus with Fuchsian singularities will be presented, providing a Conformal Field Theory expression of the solution to the corresponding linear system on the torus and of the tau function generating isomonodromic Hamiltonians, together with the identification of these quantities with objects in an appropriate four-dimensional supersymmetric gauge theory.In the last few years, following the original spirit of the works on Holonomic Quantum Fields by Jimbo, Miwa and Sato, a new approach for the solution of a Riemann-Hilbert problem and its isomonodromic deformations has been proposed by Lisovyy et al, employing tools from two dimensional Conformal Field Theory and results from localization computation of partition functions in the context of supersymmetric gauge theories. In this talk the extension of these results to the case of the torus with Fuchsian singularities will be presented, providing a Conformal Field Theory expression of the solution to the corresponding linear system on the torus and of the tau function generating isomonodromic Hamiltonians, together with the identification of these quantities with objects in an appropriate four-dimensional supersymmetric gauge theory.