Free fermions, W-algebras and isomonodromic deformations

Abstract

We consider the theory of multicomponent free massless fermions in two dimensions and use it for construction of representations of W-algebras at integer Virasoro central charges. We define the vertex operators in this theory in terms of solutions of the corresponding isomonodromy problem. We use this construction to get some new insights on tau-functions of the multicomponent Toda type hierarchies for the class of solutions, given by the isomonodromy vertex operators and get useful representation for the tau-function of isomonodromic deformations.

arXiv comment30 pages, Dedicated to 75-th birthday of Igor Tyutin

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Cited by in corpus (12)

• Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
• Monodromy dependence and connection formulae for isomonodromic tau functions
• A slow review of the AGT correspondence
• Painleve equations from Nakajima-Yoshioka blowup relations
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• Quantum spectral problems and isomonodromic deformations
• Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions
• Higher rank isomonodromic deformations and W-algebras
• Twist-field representations of W-algebras, exact conformal blocks and character identities
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
• Fredholm Pfaffian $\tau$-functions for orthogonal isospectral and isomonodromic systems