Solving the 3D Ising Model with the Conformal Bootstrap

TL;DR

This paper applies the conformal bootstrap approach to the 3D Ising model, deriving new bounds on operator dimensions and providing an efficient computational method for conformal blocks in various dimensions.

Contribution

It introduces a novel method for computing conformal blocks in any dimension and identifies the 3D Ising model as a boundary point in the conformal bootstrap parameter space.

Findings

The 3D Ising model sits at a boundary of allowed conformal data.

New bounds on higher spin operator dimensions are established.

An efficient computational approach for conformal blocks is developed.

Abstract

We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and OPE coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.