The Continuum Limit of the Schwinger-Dyson Equations of the One and Two Matrix Model with Finite Loop Length

TL;DR

This paper derives the continuum limit of Schwinger-Dyson equations for one and two matrix models without loop length expansion, aligning with string field theory equations and revealing loop operator mixing and tadpole terms.

Contribution

It introduces a novel continuum limit approach for matrix models that matches string field theory equations and uncovers loop operator mixing effects.

Findings

Equations match those proposed for string field theory in the temporal gauge.

Loop operators must mix in the two matrix model case.

Non-constant tadpole terms are determined.

Abstract

We take the continuum limit of the \sdeq s of the one and two matrix model without expanding them in the length of the loop. The resulting equations agree with those proposed for string field theory in the temporal gauge. We find that the loop operators are required to mix in the two matrix model case and determine the non-constant tadpole terms.