https://doi.org/10.1140/epjc/s10052-021-09912-0
Regular Article - Theoretical Physics
Matrix model partition function by a single constraint
1
Lebedev Physics Institute, 119991, Moscow, Russia
2
ITEP, 117218, Moscow, Russia
3
Institute for Information Transmission Problems, 127994, Moscow, Russia
4
MIPT, 141701, Dolgoprudny, Russia
5
Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164, Sofia, Bulgaria
6
ITP, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040, Vienna, Austria
a mironov@lpi.ru, mironov@itep.ru
Received:
7
June
2021
Accepted:
6
December
2021
Published online:
27
December
2021
In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of 
-operators. In this letter, we demonstrate that even more is true: a singlew-constraint is sufficient to uniquely specify the partition functions provided one assumes that it is a power series in time-variables. This substitutes the previous specifications in terms of two requirements: either a string equation imposed on the KP/Toda 
-function or a pair of Virasoro generators. This mysterious single-entry definition holds for a variety of theories, including Hermitian and complex matrix models, and also matrix models with external matrix: the unitary and cubic Kontsevich models. In these cases, it is equivalent to W-representation and is closely related to super integrability. However, a similar single equation that completely determines the partition function exists also in the case of the generalized Kontsevich model (GKM) with potential of higher degree, when the constraint algebra is a larger W-algebra, and neither W-representation, nor superintegrability are understood well enough.
© The Author(s) 2021
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