Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\boldsymbol\varepsilon$

Understand

Using numerical conformal bootstrap technology we perform a non-perturbative study of the Ising CFT and its spectrum from infinitesimal to finite values of $\varepsilon=4-d$.

• Exploiting the recent navigator bootstrap method in conjunction with the extremal functional method, we test various qualitative and quantitative features of the $\varepsilon$-expansion.
• We follow the scaling dimensions of numerous operators from the perturbatively controlled regime to finite coupling.
• We do this for $\mathbb Z_2$-even operators up to spin 12 and for $\mathbb Z_2$-odd operators up to spin 6 and find a good matching with perturbation theory.