Liouville perturbation theory for Laughlin state and Coulomb gas

TL;DR

This paper develops a Liouville field theory-based perturbation approach to analyze the generating functional of the Laughlin state on a sphere, enabling detailed study of large particle systems with complex geometries and magnetic fields.

Contribution

It introduces a novel Liouville loop perturbation theory for the Laughlin state, extending analysis beyond leading order in large N and arbitrary metrics and magnetic fields.

Findings

Quantitative analysis of the generating functional for large N.

Extension of Liouville perturbation methods to quantum Hall states.

Framework for studying inhomogeneous magnetic fields in quantum Hall systems.

Abstract

We consider the generating functional (logarithm of the normalization factor) of the Laughlin state on a sphere, in the limit of a large number of particles $N$. The problem is reformulated in terms of a perturbative expansion of a 2d QFT, resembling the Liouville field theory. We develop an analog of the Liouville loop perturbation theory, which allows us to quantitatively study the generating functional for an arbitrary smooth metric and an inhomogeneous magnetic field beyond the leading orders in large $N$.