# A functional approach to the numerical conformal bootstrap

## TL;DR

This paper introduces a functional basis approach to the 1D conformal bootstrap that converges faster and achieves high accuracy with fewer components, potentially improving higher-dimensional applications.

## Contribution

The authors develop and demonstrate a functional basis method that accelerates convergence in the numerical conformal bootstrap, outperforming traditional derivative basis techniques.

## Key findings

- Faster convergence with fewer components in the functional basis
- High accuracy achieved with minimal truncation
- Potential for application in higher-dimensional CFTs

## Abstract

We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of components can lead to extremely accurate results, in opposition to hundreds of components in the usual approach. We explain how this is a consequence of the functional basis correctly capturing the asymptotics of bound-saturating extremal solutions to crossing. We discuss how these methods can and should be implemented in higher dimensional applications.