Loops in AdS: From the Spectral Representation to Position Space II

TL;DR

This paper advances the understanding of AdS loop amplitudes by computing finite coupling 4-point functions, deriving spectral representations for ladder diagrams, and extending results to fermionic cases in position space.

Contribution

It introduces methods to compute AdS loop diagrams with fermions and extends spectral and position space techniques to new classes of diagrams.

Findings

Resummation of loop bubble diagrams yields contact diagram results.

Fermionic Witten diagrams can be derived from scalar diagrams.

Spectral representation for ladder diagrams in AdS is established.

Abstract

We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-$N$ conformal Gross Neveu model on $AdS_3$. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].