Scattering equations and virtuous kinematic numerators and dual-trace functions

140

232

In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory -the collection of putative scalar effective field theories encoding all the α ′ -expansion of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of α ′ in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The amplitude relations due to Kleiss-Kuijf as well as Bern, Johansson and one of the current authors obeyed by Z-theory amplitudes thereby apply to all α ′ -corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kinematic numerators obey the duality between color and kinematics to all orders in α ′ .

Section: Jhep06(2017)093mentioning

confidence: 99%

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

Carrasco

Mafra

Schlotterer

2017

140

232

“…It also points out a way to obtain directly the BCJ numerators [5] (also in [8] from a different perspective): expand the reduced Pfaffian by the Kleiss-Kuijf (KK) basis [9] and the coefficients are just what we want. 1 However, it is hard to find a well-controlled way to write down the final result of the expansion for arbitrary number of particles.…”

Section: Jhep04(2017)033mentioning

confidence: 99%

BCJ numerators from reduced Pfaffian

Teng

2017

103

By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the BernCarrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the (n − 2)! DDM form BCJ numerators contains exactly (n − 1)! terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most (n − 2)! − (n − 3)!, less than those of several previous constructions.

“…Regarding the relation to previous work, we should mention that a double copy construction for Einstein-Yang-Mills amplitudes was first presented in [27] for the single trace contribution, and in [28] for the complete amplitude, with results also at loop level. These double copy constructions are based on the colour-kinematics duality [26,29], whose relation to the scattering equations has been explored in [6,30,31].…”

Section: Jhep11(2015)038mentioning

confidence: 99%

New ambitwistor string theories

Casali

Geyer

Mason

et al. 2015

126

178

We describe new ambitwistor string theories that give rise to the recent amplitude formulae for Einstein-Yang-Mills, (Dirac)-Born-Infeld, Galileons and others introduced by Cachazo, He and Yuan. In the case of the Einstein-Yang-Mills amplitudes, an important role is played by a novel worldsheet conformal field theory that provides the appropriate colour factors precisely without the spurious multitrace terms of earlier models that had to be ignored by hand. This is needed to obtain the correct multitrace terms that arise when Yang-Mills is coupled to gravity.