Scattering equations, twistor-string formulas and double-soft limits in four dimensions

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

“…This formulation of scattering amplitudes makes many dimension independent properties and symmetries manifest. Especially the study of single [16,17] and multi-soft theorems [25][26][27] 2 becomes quite straightforward. Inspired by the successful study of soft theorems in CHY we will utilize the same formalism to study collinear limits beyond the leading order.…”

Section: Jhep02(2017)038mentioning

confidence: 99%

Collinear limits beyond the leading order from the scattering equations

Nandan¹,

Plefka²,

Wormsbecher³

2017

The structure of tree-level scattering amplitudes for collinear massless bosons is studied beyond their leading splitting function behavior. These near-collinear limits at sub-leading order are best studied using the Cachazo-He-Yuan (CHY) formulation of the S-matrix based on the scattering equations. We compute the collinear limits for gluons, gravitons and scalars. It is shown that the CHY integrand for an n-particle gluon scattering amplitude in the collinear limit at sub-leading order is expressed as a convolution of an (n − 1)-particle gluon integrand and a collinear kernel integrand, which is universal. Our representation is shown to obey recently proposed amplitude relations in which the collinear gluons of same helicity are replaced by a single graviton. Finally, we extend our analysis to effective field theories and study the collinear limit of the non-linear sigma model, EinsteinMaxwell-Scalar and Yang-Mills-Scalar theory.

“…It is almost impossible to perform computation beyond five points by directly solving the scattering equations due to the complicated nature of algebraic system. A few studies on the direct solutions can be found in [6][7][8][9][10][11][12][13][14][15], but restricted to four-dimension and at special kinematics. Alternative methods for evaluating CHY-integrals without explicitly solving scattering equations are proposed by several groups from different approaches.…”

Section: Jhep06(2017)133mentioning

confidence: 99%

“…There are two cycles (12) and (1)(2). For (12) cycle, the contribution is where for simplicity the notation (2.11) has been applied. For the cycle (1)(2), when using (2.3), we take the same gauge choice t = n, and get…”

Section: The Cancelation Of Higher-order Poles With Two Elementsmentioning

confidence: 99%

Understanding the cancelation of double poles in the Pfaffian of CHY-formulism

Huang

Feng

2017

For a physical field theory, the tree-level amplitudes should possess only single poles. However, when computing amplitudes with Cachazo-He-Yuan (CHY) formulation, individual terms in the intermediate steps will contribute higher-order poles. In this paper, we investigate the cancelation of higher-order poles in CHY formula with Pfaffian as the building block. We develop a diagrammatic rule for expanding the reduced Pfaffian. Then by organizing diagrams in appropriate groups and applying the cross-ratio identities, we show that all potential contributions to higher-order poles in the reduced Pfaffian are canceled out, i.e., only single poles survive in Yang-Mills theory and gravity. Furthermore, we show the cancelations of higher-order poles in other field theories by introducing appropriate truncations, based on the single pole structure of Pfaffian.