New relations for Einstein–Yang–Mills amplitudes

Stephan Stieberger,Tomasz R Taylor

doi:10.1016/j.nuclphysb.2016.09.014

Stephan Stieberger, Tomasz R Taylor

Open Access

https://doi.org/10.1016/j.nuclphysb.2016.09.014

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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.

Highlights

Tree–level Einstein–Yang–Mills (EYM) amplitudes in Yang–Mills (YM) theory with the energy-momentum tensor coupled to Einstein’s gravity offer a useful laboratory for studying the nature of gravitons
New Relations between Einstein-Yang-Mills and Yang-Mills Amplitudes In Refs. [1,2], we showed that a class of tree–level EYM amplitudes describing decays of a single graviton into N −2 gauge bosons can be written as linear combinations of pure gauge, N –particle amplitudes in which the graviton is replaced by the pair {N −1, N } of gauge bosons
We will derive monodromy relations for disk amplitudes with a single closed string inserted on the world–sheet

Summary

Introduction

Tree–level Einstein–Yang–Mills (EYM) amplitudes in Yang–Mills (YM) theory with the energy-momentum tensor (minimally) coupled to Einstein’s gravity offer a useful laboratory for studying the nature of gravitons. We discuss a superstring framework in which gauge bosons appear as massless states of open strings on D–branes and the graviton originates from a closed string. In this case, the disk amplitudes describing such scattering processes include non–minimal couplings generated by the tower of open string states populating Regge trajectories with the slope α′. We take the soft limit in which one of these particles gets no momentum while the second one takes over the whole momentum from the graviton In this way, we obtain new relations between EYM amplitudes involving N gauge bosons plus a single graviton and pure YM amplitudes involving N gauge bosons plus one additional vector boson.

New Relations between Einstein-Yang-Mills and Yang-Mills Amplitudes

World–sheet monodromy relations for mixed string amplitudes

Relations for EYM subamplitudes from string world–sheet monodromies

Conclusions