A New Framework for Higher Loop Witten Diagrams

TL;DR

This paper introduces a generalized differential representation formalism for higher loop Witten diagrams in AdS space, enabling new computations of boundary correlators beyond tree level.

Contribution

It extends the differential representation to loop diagrams using operator-valued integrals, providing a new method for calculating complex boundary correlators.

Findings

Computed three-point bubble and triangle Witten diagrams with external states of conformal dimension d

Compared bubble diagram results with position space computations

Demonstrated the formalism's effectiveness for higher loop boundary correlator calculations

Abstract

The differential representation is a novel formalism for studying boundary correlators in $(d+1)$-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of operator-valued integrals. We use the differential representation to compute three-point bubble and triangle Witten diagrams with external states of conformal dimension $\Delta=d$. We compare the former to a position space computation.