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Résumé |
In the first half of the talk, aimed at an audience including bootstrap non-experts, I will present results from the current state of the art of the numerical conformal bootstrap: bootstrapping the stress tensor, both for the 3D Ising CFT in particular and in the space of all local, unitary 3D CFTs in general. Beyond the headline result for the Ising CFT — the most precise determinations of the leading scaling dimensions and OPE coefficients yet — I will present some preliminary results in analyzing the extremal functional spectrum for the Ising CFT. As for the space of all local, unitary 3D CFTs, I will present bounds which present nontrivial and puzzling features which motivate a proposed program of “CFT Cartography.” This half will be based on arXiv:2411.15300, arXiv:2602.13383, and ongoing work.
In the second half of the talk, aimed at an audience of bootstrap experts, I will move on to discussing an alternative approach to numerically finding and studying extrema solutions of bootstrap constraints, namely the method of extremal flows. I will present the development and adaptation of that approach to a more general class of flows with apparent discontinuities. I focus on upgrading solutions of gap maximization for the spinning modular bootstrap from low to high numerical order, though the methodology is generic to a broader class of bootstrap constraints and flows. This methodology presents various nontrivialities and nuances which reflect a richness of the space of bootstrap solutions. The result is a prototype which successfully upgrades solutions in a simple test case at small scale. This half will be based on arXiv:2604.24839. |
