Virasoro OPE Blocks, Causal Diamonds, and Higher-Dimensional CFT

TL;DR

This paper introduces a formalism for Virasoro identity OPE blocks in 2D CFTs, generalizes it to higher dimensions, and derives stress tensor exchange contributions in 3D and 4D four-point correlators, advancing understanding of conformal blocks.

Contribution

It develops a new construction of Virasoro identity OPE blocks using causal diamonds and extends this approach to higher dimensions, providing a novel derivation of stress tensor exchanges.

Findings

Derived stress tensor exchange contributions in 3D and 4D four-point functions.

Proposed a formalism adaptable to higher-dimensional CFTs.

Connected OPE blocks with causal diamond integrals.

Abstract

In two-dimensional Conformal Field Theory (CFT), multi-stress tensor exchanges between probe operators give rise to the Virasoro identity conformal block, which is fixed by symmetry. The analogous object, and the corresponding organizing principles, in higher dimensions are less well understood. In this paper, we study the Virasoro identity OPE block, which is a bilocal operator that projects two primaries onto the conformal family of multi-stress tensor states. Generalizing a known construction of global OPE blocks, our formalism uses integrals over nested causal diamonds associated with two timelike-separated insertions. We argue that our construction is adaptable to higher dimensions, and use it to provide a new derivation of the single-stress tensor exchange contribution to a four-point correlator in both three and four dimensions, to leading order in the lightcone limit. We also comment on a potential description using effective reparametrization modes in four dimensions.