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Résumé |
One of the celebrated outcomes of the modern conformal bootstrap is that most likely the 3D Ising model is an (extremal) conformal field theory (CFT) that saturates the bound in a certain optimization problem. However, numerically, we don't see the different families of operators predicted from the lightcone analysis of a single crossing equation. This raises questions about whether extremal CFTs have a sparser spectrum than predicted or if numerics in the derivative basis face challenges in capturing these additional operators. This motivates us to seek an alternative basis of functionals acting on a single correlator crossing equation. These functionals are constructed using a class of 1D functionals that are dual to generalized free-field solutions. We took the first modest step to implement these functionals to numerically bootstrap higher-dimensional CFTs, demonstrating their efficiency, especially in two dimensions, where they outperform the traditional approach. Additionally, we have identified a series of new kinks in our plot that have gone unnoticed so far. In three dimensions, we reproduced the known bound, and although it is efficient, we require better control over the evaluation of these functionals to progress further. Notably, the convergence of these bounds is also better for large external dimensions in this functional basis. In this talk, I will provide an overview of this framework and discuss the general outlook. |
