Topics in soft collinear effective theory for gravity: The diffeomorphism invariant Wilson lines and reparametrization invariance

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 $\ensuremath{\lambda}$, where it has only been known to $O(\ensuremath{\lambda})$ 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 $O({\ensuremath{\lambda}}^{2})$ hard interactions of a collinear graviton are completely predicted by RPI from its $O(\ensuremath{\lambda})$ hard interactions. It is also pointed out that the multiple diffeomorphism invariances and RPI together require certain relations among $O(\ensuremath{\lambda})$ terms, thereby reducing the number of $O(\ensuremath{\lambda})$ terms that need to be fixed by matching onto the full theory in the first place.