# Bootstrapping 3D Fermions with Global Symmetries

## TL;DR

This paper applies the conformal bootstrap to 3D fermionic theories with $O(N)$ symmetry, deriving bounds on critical properties and confirming consistency with large-$N$ expansions, providing new insights into these models relevant for condensed matter physics.

## Contribution

It introduces bootstrap bounds for 3D fermions with $O(N)$ symmetry and matches these with large-$N$ expansions, offering predictions for small $N$ and connections to condensed matter systems.

## Key findings

- Bounds on scaling dimensions and central charges were obtained.
- Features in bounds coincide with $O(N)$ Gross-Neveu-Yukawa fixed points.
- Results agree with large-$N$ expansion and provide predictions at small $N$.

## Abstract

We study the conformal bootstrap for 4-point functions of fermions $\langle \psi_i \psi_j \psi_k \psi_{\ell} \rangle$ in parity-preserving 3d CFTs, where $\psi_i$ transforms as a vector under an $O(N)$ global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the $O(N)$ symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the $1/N$ expansion at large $N$ and allow us to make nontrivial predictions at small $N$. For values of $N$ for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.