The Global Sections of the Chiral de Rham Complex on a Kummer Surface

The chiral de Rham complex is a sheaf of vertex algebras <f>\Ω ^\ chM</f> on any nonsingular algebraic variety or complex manifold <f>M</f>, which contains the ordinary de Rham complex as the weight zero subspace. We show that when <f>M</f> is a Kummer surface, the algebra of global sections is isomorphic to an <f>$N=4$</f> superconformal vertex algebra with central charge 6. Previously, <f>ⁿ</f> was the only manifold where a complete description of the global section algebra was known.