Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories

TL;DR

This paper uses the numerical conformal bootstrap to explore three-dimensional cubic theories, identifying a potential conformal field theory region with implications for phase transitions, and highlighting discrepancies with previous epsilon expansion results.

Contribution

It introduces a bootstrap approach to cubic symmetric theories, revealing an isolated allowed region in parameter space suggestive of a new conformal field theory.

Findings

Identified an isolated allowed region in parameter space.

Results are in tension with previous epsilon expansion studies.

Potential applications to ferromagnetic and structural phase transitions.

Abstract

Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are probed for consistency. An isolated allowed region in parameter space is found under certain assumptions involving pushing operator dimensions above marginality, indicating the existence of a conformal field theory in this region. The obtained results have possible applications for ferromagnetic phase transitions as well as structural phase transitions in crystals. They are in tension with previous $\varepsilon$ expansion results, as noticed already in earlier work.