Generalized K$\ddot{a}$hler Geometry and current algebras in classical N=2 superconformal WZW model

TL;DR

This paper explores the connection between Generalized Kähler geometry and superconformal current algebras in the classical N=2 super WZW model, revealing geometric structures underlying superconformal symmetries.

Contribution

It establishes a link between Generalized Kähler geometry and Kac-Moody superalgebra currents in the N=2 super WZW model using Hamiltonian formalism.

Findings

Poisson homogeneous space structure is key to superconformal symmetry.

Kac-Moody currents are globally defined via biholomorphic gerbe geometry.

The geometric data determines the superalgebra symmetries.

Abstract

I examine the Generalized K$\ddot{a}$hler geometry of classical $N=(2,2)$ superconformal WZW model on a compact group and relate the right-moving and left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler geometry data using Hamiltonian formalism. It is shown that canonical Poisson homogeneous space structure induced by the Generalized K$\ddot{a}$hler geometry of the group manifold is crucial to provide $N=(2,2)$ superconformal sigma-model with the Kac-Moody superalgebra symmetries. Biholomorphic gerbe geometry is used to prove that Kac-Moody superalgebra currents are globally defined.