Gauge Boson Exchange in $AdS_{d+1}$

TL;DR

This paper analyzes gauge boson exchange amplitudes in Anti-de Sitter space, providing explicit calculations and new methods relevant for understanding the AdS/CFT correspondence and boundary conformal theories.

Contribution

It offers a concise derivation of the gauge boson propagator in AdS and develops techniques for calculating exchange amplitudes with explicit integral representations.

Findings

Amplitude exhibits power and logarithmic singularities in the gauge boson channel

Explicit integral representations for the exchange amplitude are derived

Methods have potential applications in Maldacena conjecture studies

Abstract

We study the amplitude for exchange of massless gauge bosons between pairs of massive scalar fields in Anti-de Sitter space. In the AdS/CFT correspondence this amplitude describes the contribution of conserved flavor symmetry currents to 4-point functions of scalar operators in the boundary conformal theory. A concise, covariant (Y2K-compatible) derivation of the gauge boson propagator in $\AdS_{d+1}$ is given. Techniques are developed to calculate the two bulk integrals over AdS space leading to explicit expressions or convenient, simple integral representations for the amplitude. The amplitude contains leading power and sub-leading logarithmic singularities in the gauge boson channel and leading logarithms in the crossed channel. The new methods of this paper are expected to have other applications in the study of the Maldacena conjecture.