# Bulk Phase Shift, CFT Regge Limit and Einstein Gravity

## TL;DR

This paper explores the properties of bulk phase shifts in CFTs with classical gravity duals, deriving bounds on interactions and couplings using causality, unitarity, and Regge theory, with implications for higher spin particles.

## Contribution

It provides a detailed analysis of bulk phase shifts for vector operators in large N CFTs and establishes bounds on three-point functions and non-minimal couplings based on causality and unitarity constraints.

## Key findings

- Bounds on three-point functions involving vectors and stress tensor.
- Suppression of non-minimal graviton couplings in classical gravity duals.
- Constraints on higher spin particle interactions in holographic theories.

## Abstract

The bulk phase shift, related to a CFT four-point function, describes two-to-two scattering at fixed impact parameter in the dual AdS spacetime. We describe its properties for a generic CFT and then focus on large $N$ CFTs with classical bulk duals. We compute the bulk phase shift for vector operators using Regge theory. We use causality and unitarity to put bounds on the bulk phase shift. The resulting constraints bound three-point functions of two vector operators and the stress tensor in terms of the gap of the theory. Similar bounds should hold for any spinning operator in a CFT. Holographically this implies that in a classical gravitational theory any non-minimal coupling to the graviton, as well as any other particle with spin greater than or equal to two, is suppressed by the mass of higher spin particles.

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Source: https://tomesphere.com/paper/1705.02934