# 3D CFT Archipelago from Single Correlator Bootstrap

## TL;DR

This paper demonstrates that the scaling dimensions of the lowest operators in conformal field theories can be precisely isolated using single correlator bootstrap techniques, especially by leveraging conserved currents and imposing spectral gaps.

## Contribution

It introduces a method to isolate CFTs in small regions using single correlator bootstrap and gap assumptions, including applications to supersymmetric models.

## Key findings

- Isolated regions for 3D Ising and O(N) models identified.
- Conserved currents are crucial in bootstrap equations.
- Gaps in operator spectra help fix CFTs with extended supersymmetry.

## Abstract

We show that the scaling dimensions of lowest operators in conformal field theories (CFTs) can be isolated in small and closed regions from single correlator bootstrap. We find the conserved currents play crucial roles in bootstrapping the crossing equation. By imposing a mild gap between the scaling dimensions of the conserved current and its next operator, the scaling dimensions of lowest operators are forced to lie in small isolated regions, i.e., these CFTs can be almost fixed by few lowest operators in certain channels. For CFTs with extended supersymmetry, the single correlator crossing equation involves several conserved or shorted operators and by imposing gaps in these sectors it is possible to isolate different CFTs. Specifically, we bootstrap the isolated regions corresponding to the 3D Ising model, $O(N)$ vector model, $N=1,2$ supersymmetric Ising models by introducing mild gaps in certain sectors with conserved or shorted operators.