Non-Abelian W-representation for GKM

Abstract

$W$-representation is a miraculous possibility to define a non-perturbative (exact) partition function as an exponential action of somehow integrated Ward identities on unity. It is well known for numerous eigenvalue matrix models when the relevant operators are of a kind of $W$-operators: for the Hermitian matrix model with the Virasoro constraints, it is a $W_3$-like operator, and so on. We extend this statement to the monomial generalized Kontsevich models (GKM), where the new feature is the appearance of an ordered P-exponential for the set of non-commuting operators of different gradings.

arXiv comment15 pages

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Cited by in corpus (16)

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• Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators
• $(q,t)$-deformed (skew) Hurwitz $\tau$-functions
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• $W_{1+\infty }$ and $\tilde{W}$ algebras, and Ward identities
• On character expansion and Gaussian regularization of Itzykson-Zuber measure
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• Phases in WLZZ Matrix Models
• Integrability and Matrix Models
• The ordered exponential representation of GKM using the $W_{1+\infty }$ operator
• A new kind of anomaly: on W-constraints for GKM