Topics in gravity SCET: the diff Wilson lines and reparametrization invariance

TL;DR

This paper advances gravity SCET by extending collinear Wilson lines to all orders and analyzing reparametrization invariance, which constrains the structure of the effective theory and predicts higher-order interactions.

Contribution

It extends collinear Wilson lines in gravity SCET to all orders and demonstrates how reparametrization invariance constrains the lagrangian structure and predicts higher-order interactions.

Findings

Wilson lines extended to all orders in λ

Reparametrization invariance constrains lagrangian terms

Higher-order graviton interactions predicted from lower orders

Abstract

Two topics in soft collinear effective theory (SCET) for gravitational interactions are explored. First, the collinear Wilson lines---necessary building blocks for maintaining multiple copies of diffeomorphism invariance in gravity SCET---are extended to all orders in the SCET expansion parameter $\lambda$, where it has only been known to $O(\lambda)$ in the literature. Second, implications of reparametrization invariance (RPI) for the structure of gravity SCET lagrangians are studied. The utility of RPI is illustrated by an explicit example in which $O(\lambda^2)$ hard interactions of a collinear graviton are completely predicted by RPI from its $O(\lambda)$ hard interactions. It is also pointed out that the multiple diffeomorphism invariances and RPI together require certain relations among $O(\lambda)$ terms, thereby reducing the number of $O(\lambda)$ terms that need to be fixed by matching onto the full theory in the first place.