The Berkovits Method for Conformally Invariant Non-linear Sigma-models on G/H

TL;DR

This paper applies the Berkovits method to construct symmetry currents and primaries in 2D non-linear sigma-models on Kaehler manifolds G/H, providing explicit realizations for irreducible cases.

Contribution

It introduces a variant of Wakimoto realization for affine Lie algebras using the Berkovits method on specific Kaehler manifolds G/U(1)^r.

Findings

Explicit construction of G-symmetry currents and primaries.

Application to irreducible Kaehler manifolds G/H.

Connection to Wakimoto realization of affine Lie algebra.

Abstract

We discuss 2-dimmensional non-linear sigma-models on the Kaehler manifold G/H in the first order formalisim. Using the Berkovits method we explicitly construct the G-symmetry currents and primaries, when G/H are irreducible. It is a variant of the Wakimoto realization of the affine Lie algebra using a particular reducible Kaehler manifold G/U(1)^r with r the rank of G.