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

TL;DR

This paper introduces a higher-dimensional analogue of conformal blocks using Deligne cohomology, demonstrating its finite-dimensionality on (4k+2)-dimensional disks, extending conformal field theory concepts.

Contribution

It constructs a new space of conformal blocks in higher dimensions based on projective Deligne cohomology representations, a novel extension of conformal field theory tools.

Findings

Finite-dimensionality of the constructed space on (4k+2)-dimensional disks

Explicit computation of the space for the standard disk

Extension of conformal blocks concept to higher 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.