# Generalized K\"ahler Geometry and current algebras in $SU(2)\times U(1)$ N=2 superconformal WZW model

## TL;DR

This paper explores the connection between Generalized Kähler Geometry and the current algebra structures in an N=2 superconformal WZW model on SU(2)×U(1), revealing geometric insights into the model's algebraic currents.

## Contribution

It establishes a relationship between Kac-Moody superalgebra currents and Generalized Kähler Geometry data in the context of the SU(2)×U(1) WZW model using Hamiltonian formalism.

## Key findings

- Identifies the geometric origin of superconformal currents.
- Relates algebraic currents to Generalized Kähler Geometry data.
- Provides a Hamiltonian formalism framework for the analysis.

## Abstract

We examine the Generalized K$\ddot{a}$hler Geometry of quantum N=2 superconformal WZW model on $SU(2)\times U(1)$ and relate the right-moving and left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler Geometry data of the group manifold using Hamiltonian formalism.