Spinning AdS Loop Diagrams: Two Point Functions

TL;DR

This paper introduces a systematic spectral representation method for evaluating AdS loop diagrams, specifically focusing on two-point one-loop Witten diagrams with symmetric fields, and applies it to compute anomalous dimensions in higher-spin theories.

Contribution

It develops a spectral integral approach to evaluate AdS loop diagrams, enabling analysis of higher-spin current anomalous dimensions from bubble diagrams.

Findings

Spectral representation simplifies AdS loop calculations.

Explicit computation of anomalous dimensions in higher-spin theories.

Framework applicable to arbitrary mass and spin fields.

Abstract

We develop a systematic approach to evaluating AdS loop amplitudes based on the spectral (or "split") representation of bulk-to-bulk propagators, which re-expresses loop diagrams in terms of spectral integrals and higher-point tree diagrams. In this work we focus on 2pt one-loop Witten diagrams involving totally symmetric fields of arbitrary mass and integer spin. As an application of this framework, we study the contribution to the anomalous dimension of higher-spin currents generated by bubble diagrams in higher-spin gauge theories on AdS.