Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
arXiv:1803.01701 · doi:10.1007/JHEP07(2018)177
Abstract
In this paper, we derive generalized Bern-Carrasco-Johansson relations for color-ordered Yang-Mills amplitudes by imposing gauge invariance conditions and dimensional reduction appropriately on the new discovered graphic expansion of Einstein-Yang-Mills amplitudes. These relations are also satisfied by color-ordered amplitudes in other theories such as color-scalar theory, bi-scalar theory and nonlinear sigma model (NLSM). As an application of the gauge invariance induced relations, we further prove that the three types of BCJ numerators in NLSM , which are derived from Feynman rules, Abelian Z-theory and Cachazo-He- Yuan formula respectively, produce the same total amplitudes. In other words, the three distinct approaches to NLSM amplitudes are equivalent to each other.
40pages, 2 figures
References in corpus (14)
- Minimal Basis for Gauge Theory Amplitudes
- The Momentum Kernel of Gauge and Gravity Theories
- Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
- Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
- A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
- New Relations for Einstein-Yang-Mills Amplitudes
- Einstein-Yang-Mills from pure Yang-Mills amplitudes
- New Identities among Gauge Theory Amplitudes
- Amplitude relations in heterotic string theory and Einstein-Yang-Mills
- Expansion of All Multitrace Tree Level EYM Amplitudes
- Relations for Einstein-Yang-Mills amplitudes from the CHY representation
- Graviton and gluon scattering from first principles
- A minimal approach to the scattering of physical massless bosons
- Note on symmetric BCJ numerator