How many UV theories flow to Ising? A massless bootstrap answer
ABSTRACT
The 2D Ising CFT admits two famous integrable deformations, described by a free fermion and by Zamolodchikov's E8 scattering theory. Recently, this logic has been reversed: instead of flowing down from a UV theory, one can ask which UV theories flow into a given IR CFT. A generic irrelevant deformation involves infinitely many couplings, and only fine-tuned combinations consistent with integrability lead to well-defined UV theories. This condition can be solved systematically using massless S-matrices. In this talk, we apply this program to the Ising CFT with the E8 spectrum. We find exactly four consistent UV completions, including a new "golden" flow that was not known before. Remarkably, the golden ratio of the E8 mass spectrum reappears in this new flow, which couples precisely the particle pairs with golden mass ratios, hinting that the E8 structure survives up to the UV.
