Central charge of the Virasoro algebra for supersymmetric sigma models on Calabi-Yau manifolds

Abstract

It is shown that the central charge of the Virasoro algebra for a conformally invariant supersymmetric σ-model on a Calabi-Yau manifold remains equal to its free field value to order α'⁴ despite the non-Ricci-flatness of the background metric. Various possibilities for higher loop contributions are discussed.