Vector Effective Field Theories from Soft Limits

TL;DR

The paper addresses the problem of uniquely determining vector EFTs from the infrared behavior of on-shell scattering amplitudes. It develops two complementary probes—multi-chiral soft limits in $D=4$ and dimensional reduction to scalars in general dimensions—showing that Born-Infeld (BI) theory is uniquely fixed by these soft constraints, and derives an on-shell recursion for BI amplitudes. Supersymmetry arguments further reinforce BI's uniqueness by linking the bosonic sector to a SUSY EFT with a goldstino soft zero. Extending the framework, the authors explore vector galileon-like theories and the role of dimensional reduction, illustrating both the potential and the limitations of soft-limit constraints in classifying vector EFTs. Overall, the work demonstrates a powerful amplitude-based bootstrap approach for vector theories and points to broader structures beyond BI.

Abstract

We present a bottom-up construction of vector effective field theories using the infrared structure of scattering amplitudes. Our results employ two distinct probes of soft kinematics: multiple soft limits and single soft limits after dimensional reduction, applicable in four and general dimensions, respectively. Both approaches uniquely specify the Born-Infeld (BI) model as the only theory of vectors completely fixed by certain infrared conditions which generalize the Adler zero for pions. These soft properties imply new recursion relations for on-shell scattering amplitudes in BI theory and suggest the existence of a wider class of vector effective field theories.