D=0 Matrix Model as Conjugate Field Theory

TL;DR

This paper reformulates the D=0 matrix model as a 2D nonlocal quantum field theory, revealing classical solutions, nonplanar effects, and quantum corrections that include string-perturbative and nonperturbative phenomena.

Contribution

It introduces a novel 2D nonlocal field theory formulation of the D=0 matrix model, connecting eigenvalue density dynamics with quantum and nonperturbative effects.

Findings

Classical solutions correspond to modified Dyson seas with entropy smoothing edges.

Quantum fluctuations are computable with divergences removed to all orders.

Double scaling limit simplifies quantum corrections, capturing string effects.

Abstract

The D=0 matrix model is reformulated as a 2d nonlocal quantum field theory. The interactions occur on the one-dimensional line of hermitian matrix eigenvalues. The field is conjugate to the density of matrix eigenvalues which appears in the Jevicki-Sakita collective field theory. The classical solution of the field equation is either unique or labeled by a discrete index. Such a solution corresponds to the Dyson sea modified by an entropy term. The modification smoothes the sea edges, and interpolates between different eigenvalue bands for multiple-well potentials. Our classical eigenvalue density contains nonplanar effects, and satisfies a local nonlinear Schr\"odinger equation with similarities to the Marinari-Parisi $D=1$ reformulation. The quantum fluctuations about a classical solution are computable, and the IR and UV divergences are manifestly removed to all orders. The quantum corrections greatly simplify in the double scaling limit, and include both string-perturbative and nonperturbative effects.