Rigorous bounds on irrelevant operators in the 3d Ising model CFT
Abstract
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 spin2 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 spin2 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. This both validates the EFM and shows the navigatorsearch method to be a feasible and more rigorous alternative for estimating a large part of the lowdimensional operator spectrum. We also investigate the effect of imposing sparseness conditions on all sectors at once. We find that the island does not greatly reduce in size under these assumptions. We efficiently find islands and determine their size in highdimensional parameter spaces (up to 13 parameters). This shows that using the navigator method the numerical conformal bootstrap is no longer constrained to the exploration of small parameter spaces.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.12093
 Bibcode:
 2021arXiv211112093R
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics
 EPrint:
 34 pages, 7 figures