Collective Hamiltonians with Kac-Moody Algebraic Conditions

TL;DR

This paper develops a framework for constructing collective-theory Hamiltonians constrained by Kac-Moody algebras, with explicit examples and connections to matrix models.

Contribution

It introduces a general method for building Hamiltonians with Kac-Moody algebraic constraints and explores their reduction to Wn-constraints in matrix models.

Findings

Explicit examples for sl(2)_k and sl(3)_k algebras

Framework linking hermicity to Kac-Moody constraints

Reduction to Wn-constraints for matrix models

Abstract

We describe the general framework for constructing collective--theory Hamiltonians whose hermicity requirements imply a Kac--Moody algebra of constraints on the associated Jacobian. We give explicit examples for the algebras $sl(2)_k$ and $sl(3)_k$. The reduction to $W_n$--constraints, relevant to $n$-matrix models, is described for the Jacobians.