Speaker
Description
By solving Ward identities of matrix models one can obtain their representation as generating functions of matrix elements of two-dimensional conformal theories --- conformal matrix models. Ward identities of one-matrix model --- Virasoro constraints, are solved in terms of free boson correlators. Zamolodchikov' W-algebras appear as the main constituent of multi-matrix models Ward identities with peculiar interaction --- they are solved in terms of free higher spin fields correlators. But Ward identities of two-matrix models with naive coupling turn out to be built from something closely related, though different from W-algebras. These new algebras were discovered by A. Mironov and A. Morozov in the early 1990's and got the name \(\widetilde W\)-algebras. Corresponding conformal field theories are, again, of free higher spin fields, but with non-standard normal ordering. \(\beta\)-deformation of matrix models introduces background charge into such conformal theories, though it also have interested people per se since F. Dyson. In our work we've found Ward identities for \(\beta\)-deformed two-matrix models and described their building blocks --- \(\beta\)-deformed \(\widetilde W\) algebras.
