UV/IR symmetries of the $S$-matrix and RG flow

TL;DR

This paper reveals that UV/IR symmetries of the low energy $S$-matrix in non-relativistic scattering are reflected as geometric symmetries in the RG flow of EFT couplings, providing new insights into symmetry constraints.

Contribution

It demonstrates that $S$-matrix UV/IR symmetries correspond to geometric symmetries in the RG flow of EFT couplings in various dimensions.

Findings

$S$-matrix UV/IR symmetries are geometric symmetries of RG flow

Breaking these symmetries constrains the RG flow of symmetry-breaking operators

Example shows strong constraints from symmetry breaking on EFT coefficients

Abstract

The low energy $S$-matrix which describes non-relativistic scattering arising from finite-range forces has UV/IR symmetries that are hidden in the corresponding effective field theory (EFT) action. It is shown that the $S$-matrix symmetries are manifest as geometric symmetries of the RG flow of coupling constants in the EFT action in both three and two spatial dimensions. An example is given demonstrating that UV/IR symmetry breaking in the $S$-matrix implies strong constraints on the RG flow of the coefficients of the corresponding symmetry-breaking operators in the EFT.