Bootstrapping non-unitary CFTs

TL;DR

This paper presents a novel numerical bootstrap method for non-unitary conformal field theories that does not rely on unitarity, enabling the study of a broader class of models.

Contribution

The authors develop a bootstrap strategy based on crossing symmetry and OPE data stability, applicable to non-unitary theories, and demonstrate its effectiveness on Virasoro minimal models.

Findings

Successfully reproduces known non-unitary minimal models

Provides candidate solutions for theories with central charge c>1

Achieves crossing violation levels comparable to minimal models

Abstract

We introduce a non-unitary-compatible numerical bootstrap strategy based on the statistical stability of OPE data inferred from crossing at multiple cross-ratios. For a trial spectrum, crossing determines OPE coefficients whose residual cross-ratio dependence directly measures the truncation error. This defines a scalar objective on the space of spectra, allowing bootstrap searches without imposing unitarity. Applied to two-dimensional Virasoro blocks, the method reproduces known A-series minimal models, including non-unitary examples, and yields candidate truncated solutions for c>1 with crossing violation comparable to that of minimal models. More generally, our framework provides a practical route to solving bootstrap constraints beyond the convex, unitary setting.