Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries

TL;DR

This paper develops a consistent constrained WZWN model on G/{S x U(1)^n}, establishing its algebraic structure, including the Virasoro algebra and exchange algebra of G-primaries, ensuring conformal invariance and model consistency.

Contribution

It introduces a new formulation of constrained WZWN models on G/{S x U(1)^n} with explicit algebraic structures and conformal properties, including the exchange algebra of G-primaries.

Findings

Virasoro algebra for the energy-momentum tensor is derived.

A G-primary satisfying a classical exchange algebra is constructed.

Conformal weights of constrained currents are confirmed to be zero.

Abstract

Consistently constrained WZWN models on G/{S x U(1)^n} is given by constraining currents of the WZWN models with G. Poisson brackets are set up on the light-like plane. Using them we show the Virasoro algebra for the energy-momentum tensor of constrained WZWN models. We find a G-primary which satisfies a classical exchange algebra in an arbitrary representation of G. The G-primary and the constrained currents are also shown to obey the conformal transformation with respect to the energy-momentum tensor. It is checked that conformal weight of the constrained currents is 0. This is necessary for the consistency for our formulation of constrained WZWN models.