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arXiv · hep-th/9512147

Collective field theory of the matrix-vector model

Jean Avan·Antal Jevicki
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Abstract

We construct collective field theories associated with one-matrix plus $r$ vector models. Such field theories describe the continuum limit of spin Calogero Moser models. The invariant collective fields consist of a scalar density coupled to a set of fields in the adjoint representation of $U(r)$. Hermiticity conditions for the general quadratic Hamiltonians lead to a new type of extended non-linear algebra of differential operators acting on the Jacobian. It includes both Virasoro and $SU(r)$ (included in $sl(r, {\bf C}) \times sl(r, {\bf C})$) current algebras. A systematic construction of exact eigenstates for the coupled field theory is given and exemplified.

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Jean Avan, Antal Jevicki. 1996-03-19. Collective field theory of the matrix-vector model. https://doi.org/10.1016/0550-3213(96)00147-2

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