More Holography from Conformal Field Theory

TL;DR

This paper provides evidence that conformal field theories with certain spectral properties correspond to local bulk theories in Anti-de Sitter space, by counting solutions to crossing constraints and matching interactions.

Contribution

It extends previous work by counting solutions to crossing constraints at order 1/N^2 and introduces parity odd conformal blocks, supporting the holographic duality conjecture.

Findings

Counting of solutions matches bulk interactions

Parity odd conformal blocks are introduced

Supports the conjecture of local bulk duals for certain CFTs

Abstract

We extend the work of [4] to support the conjecture that any conformal field theory with a large N expansion and a large gap in the spectrum of anomalous dimensions has a local bulk dual. We count to O(1/N^2) the solutions to the crossing constraints in conformal field theory for a completely general scalar four-point function and show that, to this order, the counting matches the number of independent interactions in a general scalar theory on Anti-de Sitter space. We introduce parity odd conformal blocks for this purpose.