The Deformed Matrix Model at Finite Radius and a New Duality Symmetry

TL;DR

This paper investigates a deformed $c=1$ matrix model at finite radius, introduces calculational methods, and uncovers a novel $R ightarrow 1/R$ duality that connects different genus contributions.

Contribution

It presents new calculational techniques for the deformed matrix model and discovers a unique duality symmetry involving genus mixing.

Findings

New duality symmetry $R ightarrow 1/R$ that mixes different genus.

Calculational methods demonstrated with specific examples.

Insights into the deformed matrix model at finite radius and non-zero cosmological constant.

Abstract

The $1/x^{2}$ deformed $c=1$ matrix model is studied at finite radius and non-zero cosmological constant. Calculational techniques are presented and illustrated in some examples. Furthermore, a new kind of $R \rightarrow 1/R$ duality is discovered which mixes different genus.