Liouville Field Theory of Fluctuating Loops

TL;DR

This paper develops a Liouville field theory approach to analyze two-dimensional fluctuating loop models, offering a geometric perspective on conformal invariance and enabling exact calculations of critical properties.

Contribution

It introduces a novel mapping of lattice loop models to Liouville field theory, providing a new method to compute critical exponents and conformal charge exactly.

Findings

Calculated conformal charge for Hamiltonian walks.

Derived critical exponents for loop models.

Established a geometric framework for conformal invariance.

Abstract

Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view of conformal invariance in two-dimensional critical phenomena and a method for calculating critical properties of loop models exactly. As an application of the method, the conformal charge and critical exponents for two mutually excluding Hamiltonian walks on the square lattice are calculated.