Loop Hodge structure and harmonic bundles

Abstract

We define the notion of a loop Hodge structure -- an infinite dimensional generalization of a Hodge structure -- and prove that a suitable variation of this object over a complex manifold is equivalent to the datum of a harmonic bundle. Hence one can study harmonic bundles using classical tools of Hodge theory, especially the existence of a period map (with values in an infinite dimensional period domain). Among other applications, we prove an integrality result for the Hitchin energy class of a harmonic bundle.