Matrix-model dualities in the collective field formulation

TL;DR

This paper demonstrates a duality between two free matrix models at large N using collective field theory, revealing a strong-weak coupling relationship and proposing a master Hamiltonian linking to the hermitian matrix model.

Contribution

It establishes a new duality between real-symmetric and quaternionic-real matrix models in the large-N limit using conformal collective field theory.

Findings

Real-symmetric matrix model is dual to quaternionic-real matrix model at large N.

A conformally invariant master Hamiltonian is constructed.

The master Hamiltonian is conjectured to correspond to the hermitian matrix model.

Abstract

We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field formulation, the duality is displayed in terms of the generators of the conformal group. The conformally invariant master Hamiltonian is constructed and we conjecture that the master Hamiltonian corresponds to the hermitian matrix model.