A twisted conformal field theory description of the Quantum Hall Effect

TL;DR

This paper develops a conformal field theory with twisted boundary conditions to model quantum Hall fluids at Jain hierarchical fillings, providing a new algebraic framework and explicit wave function representations.

Contribution

It introduces a novel twisted conformal field theory approach to describe quantum Hall states at Jain fillings, unifying charged and neutral fields within a U(1)xW_m algebra.

Findings

Constructed an effective CFT with twisted boundary conditions.

Described quantum Hall fluids at specific filling factors.

Provided explicit ground state wave functions as correlators.

Abstract

We construct an effective conformal field theory by using a procedure which induces twisted boundary conditions for the fundamental scalar fields. That allows to describe a quantum Hall fluid at Jain hierarchical filling, nu=m/(2pm+1), in terms of one charged scalar field and m-1 neutral ones. Then the resulting algebra of the chiral primary fields is U(1)xW_m. Finally the ground state wave functions are given as correlators of appropriate composite fields (a-electrons).