# One-point functions in AdS/dCFT

## TL;DR

This paper reviews recent progress in calculating one-point functions in defect conformal field theories with holographic duals, emphasizing integrability techniques and determinant formulas for overlaps.

## Contribution

It reformulates the computation of one-point functions as overlaps between Bethe states and Matrix Product States, providing determinant formulas for these overlaps.

## Key findings

- Overlap formulas enable efficient computation of one-point functions.
- Integrability techniques connect spin chains to holographic defect CFTs.
- Determinant expressions simplify complex calculations.

## Abstract

In this review we discuss recent advances in the computation of one-point functions in defect conformal field theories with holographic duals. We briefly review the appearance of integrable spin chains in N=4 super Yang--Mills theory and reformulate the problem of computing one-point functions to determining overlaps between Bethe states and a Matrix Product State. We will then demonstrate how these overlaps can be computed by determinant formulas. This work is based on lectures given at the Young Researchers Integrability School and Workshop 2018. To appear in a special issue of J. Phys. A.