Conformal Bootstrap Deformations

TL;DR

This paper develops an efficient method to explore the space of conformal field theories by deforming extremal solutions in the bootstrap, revealing connections between known models and non-unitary theories across dimensions.

Contribution

It introduces a new algorithm for converging to extremal bootstrap solutions and demonstrates their continuous deformation, linking different CFTs and extending to non-unitary cases.

Findings

Connected Ising and Yang-Lee models in 2D.

Deformed solutions align with epsilon-expansion in 3D.

Method enables exploration of non-unitary CFTs.

Abstract

We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal solution corresponding to the boundary of allowed regions in the parameter space of CFTs. Furthermore, by deforming these solutions, we demonstrate that certain solutions corresponding to known theories are continuously connected. Employing these methods, we will explore the space of non-unitary CFTs in the context of modular as well as correlation function bootstrap. In two dimensions, we show that the extremal solution corresponding to the Ising model is connected to that of the Yang-Lee minimal model. By deforming this solution to three dimensions, we provide evidence that the CFT data obtained in this way is compatible with the $\epsilon$-expansion for a non-unitary theory.