Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II

TL;DR

This paper uses the numerical conformal bootstrap to identify a unique allowed region in 3D cubic symmetric CFTs, revealing the existence of a new 'Platonic CFT' alongside the Ising model.

Contribution

It performs a detailed bootstrap scan in 3D cubic theories, discovering an isolated allowed region that includes a novel CFT, expanding understanding of these models.

Findings

Identified an isolated allowed region in 3D cubic CFT parameter space.

Confirmed the coexistence of the Platonic CFT and the 3D Ising model within this region.

Provided nonperturbative evidence for a new cubic symmetric CFT.

Abstract

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed "Platonic CFT". In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).