Amplitudes in N=4 SYM -- Simplicity and structure in symbols

Abstract: Scattering amplitudes are central to understanding particle interactions in quantum field theory, serving as a bridge between theoretical predictions and experimental observations. In this talk, I will first introduce modern approaches to computing scattering amplitudes that go beyond traditional Feynman-diagram techniques, such as on-shell recursion relations and unitarity-based methods. These methods reveal a remarkable simplicity in the analytic structure of amplitudes, made manifest by the symbol. I will then turn to planar N=4 super Yang–Mills theory, which provides an ideal setting to explore the connections between generalized unitarity, Landau analysis and cluster algebras. In dimensional regularization, the symbol of the one-loop amplitude decomposes into a part controlled by maximal cuts, where Landau singularities of nested cuts order the symbol entries, and a residual sector. Cancellations of letters from individual box integrals are explained by the two-mass triangle relations among box coefficients. Finally, I will discuss the cluster-algebraic properties of the amplitude. This talk is based on arXiv:2609.05716 with R. Britto and M. Parisi.

general relativity and quantum cosmologyHEP - experimentHEP - latticeHEP - phenomenologyHEP - theory

Audience: researchers in the topic

Comments: In person only.

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