More constraining conformal bootstrap

TL;DR

This paper extends the conformal bootstrap method to a broader class of conformal field theories, including non-unitary ones, enabling the calculation of operator dimensions without free parameters, and applies it to the Yang-Lee edge singularity.

Contribution

It introduces a generalized bootstrap approach applicable to non-unitary CFTs using fusion algebra, and computes operator dimensions for the Yang-Lee edge singularity from first principles.

Findings

Calculated lowest scaling dimensions for Yang-Lee edge in 3D and 4D.

Results agree with recent numerical estimates.

Validated method on the 3D critical Ising model.

Abstract

Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories (CFT) in diverse space-time dimensions. It appears that the calculations can be done only for theories lying at the boundary of the allowed parameter space. Here it is pointed out that a similar method can be applied to a larger class of CFT's, whether unitary or not, and no free parameter remains, provided we know the fusion algebra of the low lying primary operators. As an example we calculate using first principles, with no phenomenological input, the lowest scaling dimensions of the local operators associated with the Yang-Lee edge singularity in three and four space dimensions. The edge exponents compare favorably with the latest numerical estimates. A consistency check of this approach on the 3d critical Ising model is also made.