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 Z 2 -even scalar operators and with a dimension below 6 we find a narrow allowed interval for ∆ , λ σσ and λ . With similar assumptions in the Z 2 -even spin-2 and the Z 2 -odd scalar sectors we are also able to constrain: the central charge c T ; the OPE data ∆ T , λ T and λ σσT of the second spin-2 operator; and the OPE data ∆ σ and λ σ σ of the second 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 navigator-search method to be a feasible and more rigorous alternative for estimating a large part of the low-dimensional 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 high-dimensional 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.

Navigating through the O(N) archipelago

“…The main goal of this paper will be to lay out a method that aims to address the first concern. To follow the O(N ) islands through the (d, N ) plane, we will invoke the newly-developed navigator method of [1] (see also [19][20][21] for recent works using the navigator method). If x denotes the set of parameters to scan over in a certain bootstrap setup, a navigator function N (x) is a function which is positive oustide of the allowed regions for x, and negative inside.…”

Mixed correlator dispersive CFT sum rules

“…It would be interesting to study this mixed correlator functional matrix more extensively. Moreover, it would be interesting to test whether navigator functions [47,48] built from dispersive functionals may be more effective.…”

Mixed Correlator Dispersive CFT Sum Rules

“…Such a construction would also serve to build better functionals described at the beginning of the previous subsection. Moreover, it would be interesting to test whether navigator functions [46,47] built from dispersive functionals may be more effective.…”