Collective field theory of the matrix-vector model

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 $sl(r,\mathbf{C})\times sl(r,\mathbf{C})$) current algebras. A systematic construction of exact eigenstates for the coupled field theory is given and exemplified.

OLatex file, 20 pages, no figures. Misprints corrected, references added; reformulation of the constraint algebra and additional Comments on its structure; additional Comments on the structure of the continuum limit; Nuclear Physics B, to appear

References in corpus (15)

• Yang-Baxter equation in spin chains with long range interactions
• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra
• Spinons in Conformal Field Theory
• Density Correlation Functions in Calogero Sutherland Models
• Yangian Symmetry in Conformal Field Theory
• Exact Yangian Symmetry in the Classical Euler-Calogero-Moser Model
• Loop Space Hamiltonians And Field Theory Of Non-Critical Strings
• Anyon Basis of c=1 Conformal Field Theory
• String Field Theory in the Temporal Gauge
• LOOP SPACE HAMILTONIAN FOR $c\le 1$ OPEN STRINGS
• Observable algebra for the rational and trigonometric Euler Calogero Moser models
• Temporal-gauge String Field with Open Strings
• Collective Hamiltonians with Kac-Moody Algebraic Conditions
• Loop Equations as a Generalized Virasoro Constraints

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