Geometric Frameworks for Effective Field Theories

Speaker: Alan Lee

Date: Monday November 27, 2023

Time: 4:00 – 5:00 pm

Location: 472 Willamette Hall

Abstract: Field-redefinition invariant properties of EFTs, such as scattering amplitudes, can be captured via geometric techniques. However, the lack of derivative coordinates in conventional Riemannian field space limits its applicability. In this talk, I will discuss how field derivatives can be incorporated for scalar theories by enlarging horizontal field space in vertical directions, giving rise to the tangent and jet bundles. The tangent bundle induces a class of non-Riemannian horizontal connections that simplify certain covariant amplitude expressions. Moreover, a vertical torsion component comprises higher-point Wilson coefficients and is thus constrained by positivity and unitarity bounds. In this sense, the tangent bundle geometry reflects new information on the EFT not afforded by Riemannian field space. Meanwhile, the jet bundle further extends the vertical construction to accommodate arbitrary theories, and represents a complete framework for describing covariant EFT physics.