Renormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram

TL;DR

This paper uses renormalization group analysis to study modular invariant Coulomb gas and Sine-Gordon theories, establishing their flow diagrams and critical behaviors, and draws parallels with the quantum Hall phase diagram.

Contribution

It introduces a modular invariant RG framework for Coulomb gas and Sine-Gordon models, connecting their flow diagrams to quantum Hall transitions.

Findings

Established the flow diagram from scaling equations.

Derived critical behaviors at transition points.

Drawn analogy with quantum Hall phase diagram.

Abstract

Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.