# Asymptotic one-point functions in AdS/dCFT

## TL;DR

This paper extends the integrability approach to compute higher-loop one-point functions in AdS/dCFT, providing an asymptotic formula that matches string theory results in a specific limit.

## Contribution

It introduces a natural asymptotic generalization of the tree-level formula for one-point functions to higher loops in AdS/dCFT, including a novel amputated matrix product state.

## Key findings

- The asymptotic formula encodes one-loop corrections with a flux-dependent factor.
- Explicit computation confirms the formula's accuracy for non-protected operators.
- Results agree with dual string theory calculations up to wrapping order in a double-scaling limit.

## Abstract

We take the first step in extending the integrability approach to one-point functions in AdS/dCFT to higher loop orders. More precisely, we argue that the formula encoding all tree-level one-point functions of SU(2) operators in the defect version of N=4 SYM theory, dual to the D5-D3 probe-brane system with flux, has a natural asymptotic generalization to higher loop orders. The asymptotic formula correctly encodes the information about the one-loop correction to the one-point functions of non-protected operators once dressed by a simple flux-dependent factor, as we demonstrate by an explicit computation involving a novel object denoted as an amputated matrix product state. Furthermore, when applied to the BMN vacuum state, the asymptotic formula gives a result for the one-point function which in a certain double-scaling limit agrees with that obtained in the dual string theory up to wrapping order.