New Relations for Einstein-Yang-Mills Amplitudes

TL;DR

This paper derives new relations connecting Einstein-Yang-Mills amplitudes with pure Yang-Mills amplitudes, revealing U(1) decoupling and monodromy relations through string theory embeddings, advancing understanding of gauge-gravity interactions.

Contribution

It introduces novel relations for EYM amplitudes involving a graviton and gauge bosons, and derives monodromy relations from string theory that unify open and closed string amplitudes.

Findings

EYM amplitudes satisfy U(1) decoupling relations similar to Yang-Mills.

New monodromy relations for mixed open-closed string amplitudes.

Field-theory limit reproduces U(1) decoupling relations for EYM.

Abstract

We obtain new relations between Einstein-Yang-Mills (EYM) amplitudes involving N gauge bosons plus a single graviton and pure Yang-Mills amplitudes involving N gauge bosons plus one additional vector boson inserted in a way typical for a gauge boson of a "spectator" group commuting with the group associated to original N gauge bosons. We show that such EYM amplitudes satisfy U(1) decoupling relations similar to Kleiss-Kuijf relations for Yang-Mills amplitudes. We consider a D-brane embedding of EYM amplitudes in the framework of disk amplitudes involving open and closed strings. A new set of monodromy relations is derived for mixed open-closed amplitudes with one closed string inserted on the disk world-sheet and a number of open strings at the boundary. These relations allow expressing the latter in terms of pure open string amplitudes and, in the field-theory limit, they yield the U(1) decoupling relations for EYM amplitudes.