Rigorous bounds on irrelevant operators in the 3d Ising model CFT

Understand

We use the recently developed navigator method to obtain rigorous upper and lower bounds on new OPE data in the 3d Ising CFT.

• For example, assuming that there are only two $\mathbb{Z}_2$-even scalar operators $\epsilon$ and $\epsilon'$ with a dimension below 6 we find a narrow allowed interval for $\Delta_{\epsilon'}$, $\lambda_{\sigma\sigma\epsilon'}$ and $\lambda_{\epsilon\epsilon\epsilon'}$.
• With similar assumptions in the $\mathbb{Z}_2$-even spin-2 and the $\mathbb{Z}_2$-odd scalar sectors we are also able to constrain: the central charge $c_T$; the OPE data $\Delta_{T'}$, $\lambda_{\epsilon\epsilon T'}$ and $\lambda_{\sigma\sigma T'}$ of the second spin-2 operator; and the OPE data $\Delta_{\sigma'}$ and $\lambda_{\sigma\epsilon\sigma'}$ of the second $\mathbb{Z}_2$-odd scalar.
• We compare the rigorous bounds we find with estimates that have been previously obtained using the extremal functional method (EFM) and find a good match.