An analogue of the space of conformal blocks in $(4k + 2)$-dimensions

Abstract

Based on projective representations of smooth Deligne cohomology groups, we introduce an analogue of the space of conformal blocks to compact oriented $(4k + 2)$-dimensional Riemannian manifolds with boundary. For the standard $(4k + 2)$-dimensional disk, we compute the space concretely to prove that its dimension is finite.