Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite ε

Using numerical conformal bootstrap technology we perform a non-perturbative study of the Ising CFT and its spectrum from infinitesimal to finite values $\varepsilon=4-d$. Exploiting recent navigator method in conjunction with extremal functional method, test various qualitative quantitative features $\varepsilon$-expansion. We follow scaling dimensions numerous operators perturbatively controlled regime coupling. do this for $\mathbb Z_2$-even up spin 12 Z_2$-odd 6 find good matching perturbation theory. In coupling observe two whose approach each other then repel, phenomenon known as level repulsion which can be analyzed via operator mixing. Our work improves on previous studies both increased precision number studied, is first bootstrap.