AdS Box Graphs, Unitarity and Operator Product Expansions

TL;DR

This paper introduces a singularity analysis method for conformal graphs in AdS/CFT, showing that scalar AdS box graphs share critical exponents with their CFT counterparts, supporting the Maldacena hypothesis.

Contribution

It develops a new technique for analyzing conformal graphs' singularities, applicable to AdS supergravity, and demonstrates structural similarities between AdS and CFT box graphs.

Findings

AdS and CFT box graphs have identical critical exponents.

External fields couple to the same conformal blocks in both theories.

Supports the Maldacena hypothesis through structural analysis.

Abstract

We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis.