More Holography from Conformal Field Theory

TL;DR

The paper extends the program of relating large-N CFTs with a gap in anomalous dimensions to local AdS-like bulk theories by counting crossing-solution data for a general scalar four-point function, including parity-odd blocks in 2d. It develops both degenerate and generic cases, showing that the number of independent crossing-consistent solutions precisely matches the number of independent bulk interactions to order 1/N^2, thereby supporting a local bulk dual description. The analysis uses detailed conformal block technology, OPE structure, and branch-cut projections to establish a robust bulk-boundary counting agreement. The results strengthen the entanglement between boundary crossing constraints and bulk locality and lay groundwork for future extensions to gravitons and 3D 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.