# Non-Abelian currents bootstrap

## TL;DR

This paper applies numerical conformal bootstrap to study correlation functions of non-Abelian conserved currents in 3D conformal field theories, deriving bounds on operator dimensions and constraining theories like QED$_3$.

## Contribution

It introduces a framework for analyzing non-Abelian currents in 3D CFTs and provides new bounds and constraints on operator spectra, especially for large-$N$ theories.

## Key findings

- Bounds on operator dimensions for $SU(N)$ and $O(N)$ symmetries.
- Identification of features corresponding to fermionic QED$_3$.
- Small allowed region ('island') where QED$_3$ resides.

## Abstract

We initiate the study of correlation functions of non-Abelian spin-1 conserved current in three dimensional conformal field theories using numerical conformal bootstrap. We discuss the general framework and apply it to the particular cases of $SU(N)$ and $O(N)$ global symmetry. In both cases we obtain general bounds on operator dimensions. In the large-$N$ limit our bounds show features in correspondence of the expected position of fermionic QED$_3$ in three dimensions, as well as other interesting theories. By imposing gaps inspired by the spectrum of QED$_3$ at large-$N$, we manage to restrict the plane of certain operator dimensions to a small island, where QED$_3$ must live.