Bootstrapping the O(N) Archipelago

TL;DR

This paper uses the conformal bootstrap to analyze 3d CFTs with O(N) symmetry, constraining operator dimensions and determining current two-point functions, with implications for condensed matter physics.

Contribution

It introduces a bootstrap approach for mixed correlators in 3d O(N) models, identifying small allowed regions for operator dimensions and rigorously computing current two-point functions.

Findings

Operator dimensions confined to small islands

Rigorous determination of current two-point functions in O(2) and O(3) models

Applications to transport phenomena in condensed matter systems

Abstract

We study 3d CFTs with an $O(N)$ global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension $O(N)$ vector $\phi_i$ and the lowest dimension $O(N)$ singlet $s$, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions $(\Delta_\phi, \Delta_s)$ to lie inside small islands. We also make rigorous determinations of current two-point functions in the $O(2)$ and $O(3)$ models, with applications to transport in condensed matter systems.