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We study the relation between class S theories on punctured tori andisomonodromic deformations of flat SL(N) connections on the two dimensionaltorus with punctures. Turning on the self dual $\Omega$-background correspondsto a deautonomization of the Seiberg-Witten integrable system which implies aspecific time dependence in its Hamiltonians. We show that the corresponding$\tau$-function is proportional to the dual gauge theory partition function,the proportionality factor being a non trivial function of the solution of thedeautonomized Seiberg-Witten integrable system. This is obtained by mapping theisomonodromic deformation problem to $W_N$ free fermion correlators on thetorus.

Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus