# Two-point functions of SU(2)-subsector and length-two operators in dCFT

## TL;DR

This paper computes specific two-point functions in N=4 SYM with a defect, revealing simplified expressions by mapping contractions to spin-chain operators, advancing understanding of operator interactions in dCFT.

## Contribution

It introduces a novel approach to evaluate two-point functions involving length-two operators in the SU(2)-subsector of dCFT, connecting them to known one-point function formulas.

## Key findings

- Derived simple expressions for two-point functions involving length-two operators.
- Mapped contractions to spin-chain operators, simplifying calculations.
- Connected two-point functions to existing one-point function formulas.

## Abstract

We consider a particular set of two-point functions in the setting of N = 4 SYM with a defect, dual to the fuzzy-funnel solution for the probe D5-D3-brane system. The two-point functions in focus involve a single trace operator in the SU(2)-subsector of arbitrary length and a length-two operator built out of any scalars. By interpreting the contractions as a spin-chain operator, simple expressions were found for the leading contribution to the two-point functions, mapping them to earlier known formulas for the one-point functions in this setting.