# The Mellin Formalism for Boundary CFT$_d$

## TL;DR

This paper extends the Mellin representation to boundary and interface conformal field theories, providing a systematic analysis of Witten diagrams and demonstrating that geodesic Witten diagrams reproduce interface CFT conformal blocks.

## Contribution

It introduces a Mellin formalism for boundary and interface CFTs and shows how geodesic Witten diagrams generate conformal blocks in these setups.

## Key findings

- Mellin representation extended to boundary and interface CFTs
- Geodesic Witten diagrams reproduce interface CFT conformal blocks
- Systematic analysis of Witten diagrams in holographic interface models

## Abstract

We extend the Mellin representation of conformal field theory (CFT) to allow for conformal boundaries and interfaces. We consider the simplest holographic setup dual to an interface CFT - a brane filling an $AdS_{d}$ subspace of $AdS_{d+1}$ - and perform a systematic study of Witten diagrams in this setup. As a byproduct of our analysis, we show that geodesic Witten diagrams in this geometry reproduce interface CFT$_d$ conformal blocks, generalizing the analogous statement for CFTs with no defects.