On determinant representation and integrability of Nekrasov functions

Understand

Conformal blocks and their AGT relations to LMNS integrals and Nekrasov functions are best described by "conformal" (or Dotsenko-Fateev) matrix models, but in non-Gaussian Dijkgraaf-Vafa phases, where different eigenvalues are integrated along different contours.

• In such matrix models, the determinant representations and integrability are restored only after a peculiar Fourier transform in the numbers of integrations.
• From the point of view of conformal blocks, this is Fourier transform w.r.t.
• the intermediate dimensions and this explains why such quantities are expressed through tau-functions in Miwa parametrization, with external dimensions playing the role of multiplicities.