Higher rank isomonodromic deformations and W-algebras

Abstract

We construct the general solution of a class of Fuchsian systems of rank $N$ as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$. The simplest example is given by the tau function of the Fuji-Suzuki-Tsuda system, expressed as a Fourier transform of the 4-point conformal block with respect to intermediate weight. Along the way, we generalize the result of Bowcock and Watts on the minimal set of matrix elements of vertex operators of the $W_N$-algebra for generic central charge and prove several properties of semi-degenerate vertex operators and conformal blocks for $c=N-1$.

31 pages, 1 figure

References in corpus (5)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Correlation functions in conformal Toda field theory I
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Cited by in corpus (8)

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• Riemann-Hilbert correspondence and blown up surface defects
• Quantum spectral problems and isomonodromic deformations
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• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• On a 5D UV completion of Argyres-Douglas theories
• Fredholm Pfaffian $\tau$-functions for orthogonal isospectral and isomonodromic systems
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux