Wk structure of A from covariant construction of Kac-Moody algebras

Abstract

W k structure underlying the transverse realization of SU(2) at level k is analyzed. Extension of the equivalence existing between covariant and lightcone gauge realization of affine Kac-Moody algebra to W k algebras is given. Higher spin generators related to parafermions are extracted from the operator product algebra of the generators and are showed to be written in terms of only one free boson compactified on a circle.

A Conformal Field Theory Description of the Paired and Parafermionic States in the Quantum Hall Effect

“…while the higher integer spin operators generating the full parafermionic W m algebra [16] was given in terms of the φ j (z|m, 2) fields in [14]. Notice that the vacuum expectation value of T ψ is zero due to the cancellation between the second and the third term in eq.…”

CONFORMAL FIELD THEORY ON Zk-SURFACES WITH EXCHANGE INTERACTIONS

“…5 give also a strong evidence of the integrability of the theory on the corresponding Riemann surface, due to the existence of a nontrivial extended symmetry (W k algebra).…”

“…5, it also follows that further null fields are present in this case. They are responsible for the closure of a higher spin fields extension of the chiral algebra of the untwisted fields (the W k algebra).…”