# Bootstrapping line defects in $\mathcal{N}=2$ theories

## TL;DR

This paper applies bootstrap techniques to study half-BPS line defects in 4D $ ext{N}=2$ superconformal theories, deriving new superconformal blocks, setting up crossing equations, and providing numerical and analytical insights into defect CFT data.

## Contribution

It constructs a superspace framework and superconformal blocks for defect CFTs, and offers both numerical bounds and an analytic perturbative solution for line defects in $ ext{N}=2$ theories.

## Key findings

- Numerical bounds on defect CFT data consistent with known solutions.
- New superconformal blocks for defect correlation functions.
- Analytic perturbative solution capturing strong coupling defect behavior.

## Abstract

We study half-BPS line defects in $\mathcal{N}=2$ superconformal theories using the bootstrap approach. We concentrate on local excitations constrained to the defect, which means the system is a $1d$ defect CFT with $\mathfrak{osp}(4^*|2)$ symmetry. In order to study correlation functions we construct a suitable superspace, and then use the Casimir approach to calculate a collection of new superconformal blocks. Special emphasis is given to the displacement operator, which controls deformations orthogonal to the defect and is always present in a defect CFT. After setting up the crossing equations we proceed with a numerical and analytical bootstrap analysis. We obtain numerical bounds on the CFT data and compare them to known solutions. We also present an analytic perturbative solution to the crossing equations, and argue that this solution captures line defects in $\mathcal{N}=2$ gauge theories at strong coupling.