Geometrizing Effective Field Theories

by Xu-Xiang Li (U Utah)

Tuesday 27 May 2025, 15:00 → 16:00 Europe/Berlin

SR2

The redundancy of field redefinition is a major obstacle in the Lagrangian formulation of effective field theories (EFTs), often obscuring the underlying physics. The analogy between field redefinitions and coordinate transformations suggests that EFTs may admit a geometric reformulation that renders their physical content more transparent. Focusing on the scattering amplitudes as geometric invariants, we demonstrate that tree-level amplitudes can be constructed from on-shell covariant building blocks. In theories with up to two derivatives, these building blocks reduce to the curvature tensor, the scalar potential, and their covariant derivatives. Similar building blocks are shown to appear also at one-loop level. This geometric perspective offers new insights on the structure of EFT amplitudes and moves towards a fully geometric formulation of EFTs.