Bootstrapping the 3d Ising Stress Tensor

TL;DR

This paper advances the numerical conformal bootstrap method to precisely compute critical 3d Ising model observables, including scaling dimensions and OPE coefficients, by analyzing mixed correlators involving key operators.

Contribution

It introduces new high-precision determinations of critical exponents and OPE coefficients for the 3d Ising model using improved bootstrap algorithms and software.

Findings

Precise scaling dimensions: Δσ and Δε

Accurate OPE coefficients involving σ, ε, and Tμν

Enhanced algorithms and software tools for bootstrap

Abstract

We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators $\sigma$ and $\epsilon$, and the stress tensor $T_{\mu\nu}$. We obtain new precise determinations of scaling dimensions $(\Delta_\sigma, \Delta_\epsilon) = (0.518148806(24), 1.41262528(29))$ as well as OPE coefficients involving $\sigma$, $\epsilon$, and $T_{\mu\nu}$. We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap.