Generalized Kähler geometry and current algebras in classical N=2 superconformal WZW model

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I examine the Generalized Kähler (GK) geometry of classical [Formula: see text] superconformal WZW model on a compact group and relate the right-moving and left-moving Kac–Moody superalgebra currents to the GK geometry data using biholomorphic gerbe formulation and Hamiltonian formalism. It is shown that the canonical Poisson homogeneous space structure induced by the GK geometry of the group manifold is crucial to provide [Formula: see text] superconformal [Formula: see text]-model with the Kac–Moody superalgebra symmetries. Then, the biholomorphic gerbe geometry is used to prove that Kac–Moody superalgebra currents are globally defined.