Soft-collinear gravity with fermionic matter

TL;DR

This paper extends the soft-collinear gravity effective field theory to include fermionic matter, incorporating local Lorentz symmetry and deriving the corresponding Wilson lines, while preserving the core structure of the theory.

Contribution

It introduces the treatment of fermionic matter in soft-collinear gravity, including local Lorentz symmetry and Wilson lines, generalizing the existing scalar matter framework.

Findings

Incorporates fermionic matter into soft-collinear gravity

Derives Wilson lines associated with local Lorentz symmetry

Maintains the core structure of soft-collinear gravity with fermions

Abstract

We extend the effective field theory for soft and collinear gravitons to interactions with fermionic matter fields. The full theory features a local Lorentz symmetry in addition to the usual diffeomorphisms, which requires incorporating the former into the soft-collinear gravity framework. The local Lorentz symmetry gives rise to Wilson lines in the effective theory that strongly resemble those in SCET for non-abelian gauge interactions, whereas the diffeomorphisms can be treated in the same fashion as in the case of scalar matter. The basic structure of soft-collinear gravity, which features a homogeneous soft background field, giving rise to a covariant derivative and multipole-expanded covariant Riemann-tensor interactions, remains unaltered and generalises in a natural way to fermion fields.