A Remark on the Renormalization Group Equation for the Penner Model

TL;DR

This paper derives a renormalization group equation for the Penner matrix model, enabling the extraction of critical couplings and gamma_string, and confirms its consistency with known logarithmic corrections.

Contribution

It introduces a direct differentiation method to derive the RG equation for the Penner model, matching known critical values and corrections.

Findings

Correct critical coupling values obtained

Gamma_string consistent with known results

Logarithmic corrections for g=0,1 confirmed

Abstract

It is possible to extract values for critical couplings and gamma_string in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a ``renormalization group equation'' for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and gamma_string and is consistent with the logarithmic corrections present for g=0,1.