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Description
The modern on-shell approach to scattering amplitudes has revolutionized perturbative quantum field theory by working directly with observables to bypass redundancies. Despite the program’s success, an on-shell understanding of the Renormalization Group (RG), which describes how physical observables change with energy scale, is lacking. In this talk, I will propose a bootstrap approach to the RG based entirely on on-shell principles, without reference to Feynman diagrams or counterterms. I will introduce the Unitarity Flow Conjecture, which states that the identities needed to derive RG equations are implied by the unitarity of the S-matrix. I will demonstrate this to subleading logarithm order in massless λφ^4 theory and discuss the broader applicability.