The Critical Point of Unoriented Random Surfaces with a Non-Even Potential

TL;DR

This paper investigates a discrete model of unoriented random surfaces with a cubic potential, revealing a recursion relation and a Miura transformation connecting oriented and unoriented surface contributions in the double-scaling limit.

Contribution

It introduces a recursion relation for the partition function of a real symmetric matrix model with cubic interaction and identifies a Miura transformation linking oriented and unoriented surfaces.

Findings

Recursion relation for the partition function was derived.

Double-scaling limit leads to a Miura transformation.

Connection between oriented and unoriented surface contributions established.

Abstract

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double-scaling limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a cuartic interaction.