Free Field Realization of $WBC_{n}$ and $WG_{2}$ algebras

TL;DR

This paper constructs free field realizations of certain W-algebras derived from affine Lie algebras of non-simply laced types using BRST-cohomology and quantum Hamiltonian reduction, revealing dualities among these algebras.

Contribution

It provides explicit free field realizations for Wg-algebras of types B2, B3, C3, and G2, and demonstrates duality between WC3 and WB3 at the quantum level.

Findings

Explicit free field realizations for Wg-algebras of specified types.

Identification of duality between WC3 and WB3 algebras.

Application of BRST-cohomology in non-simply laced cases.

Abstract

We study the BRST-cohomology in the quantum hamiltonian reduction of affine Lie algebras of non-simply laced type. We obtain the free field realization of the $W{\bf g}$-algebra for $\bg=B_{2}$, $B_{3}$, $C_{3}$ and $G_{2}$. The $WC_{3}$ algebra is shown to be equal to the $WB_{3}$ algebra at the quantum level by duality transformation.