# From bulk loops to boundary large-N expansion

## TL;DR

This paper analyzes the analytic structure of loop Witten diagrams in Euclidean AdS, revealing how their singularities relate to cuts and factorization, and connects these findings to large-N boundary theories.

## Contribution

It introduces a detailed analysis of the singularities and factorization properties of loop Witten diagrams, extending the understanding of their structure in AdS/CFT.

## Key findings

- Singularities correspond to diagram cuts and factorize into subdiagram coefficients.
- The analysis reproduces relations consistent with large-N boundary theories.
- Method can be extended to more complex diagrams.

## Abstract

We study the analytic structure of loop Witten diagrams in Euclidean AdS represented by their conformal partial wave expansions. We show that, as in flat space, amplitude's singularities are associated with non-trivial cuts of the diagram and factorize into products of the coefficient functions for the subdiagrams resulting from these cuts. We consider an example of a one-loop four-point diagram in detail and then briefly discuss how the procedure can be extended to more general diagrams. Finally, we show that this analysis reproduces simple relations that follow from the large-N considerations on the boundary.