The ^sl(2)+^sl(2)/^sl(2) Coset Theory as a Hamiltonian Reduction of ^D(2|1;\alpha)

TL;DR

This paper demonstrates that a specific coset conformal field theory can be derived as a Hamiltonian reduction of an exceptional affine Lie superalgebra, linking it to quantum groups and W algebras.

Contribution

It establishes a new connection between the ^sl(2)+^sl(2)/^sl(2) coset and the quantum Hamiltonian reduction of ^D(2|1;\alpha), revealing the structure of the associated W algebra.

Findings

The coset is a quantum Hamiltonian reduction of ^D(2|1;\alpha).

The W algebra is the commutant of the quantum group U_qD(2|1;\alpha).

Provides a new perspective on the algebraic structure of this coset theory.

Abstract

We show that the coset ^sl(2)+^sl(2)/^sl(2) is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra ^D(2|1;\alpha) and that the corresponding W algebra is the commutant of the U_{q}D(2|1;\alpha) quantum group.