The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps

DOI10.1007/JHEP09(2018)125zbMATH Open1398.81255arXiv1805.11111WikidataQ129209073 ScholiaQ129209073MaRDI QIDQ1797358

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Publication date: 19 October 2018

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Abstract: We present new formulas for $n$-particle tree-level scattering amplitudes of six-dimensional $mathcalN=(1,1)$ super Yang-Mills (SYM) and $mathcalN=(2,2)$ supergravity (SUGRA). They are written as integrals over the moduli space of certain rational maps localized on the $(n-3)!$ solutions of the scattering equations. Due to the properties of spinor-helicity variables in six dimensions, the even-$n$ and odd-$n$ formulas are quite different and have to be treated separately. We first propose a manifestly supersymmetric expression for the even-$n$ amplitudes of $mathcalN=(1,1)$ SYM theory and perform various consistency checks. By considering soft-gluon limits of the even-$n$ amplitudes, we deduce the form of the rational maps and the integrand for $n$ odd. The odd-$n$ formulas obtained in this way have a new redundancy that is intertwined with the usual $extSL(2,mathbbC)$ invariance on the Riemann sphere. We also propose an alternative form of the formulas, analogous to the Witten-RSV formulation, and explore its relationship with the symplectic (or Lagrangian) Grassmannian. Since the amplitudes are formulated in a way that manifests double-copy properties, formulas for the six-dimensional $mathcalN=(2,2)$ SUGRA amplitudes follow. These six-dimensional results allow us to deduce new formulas for five-dimensional SYM and SUGRA amplitudes, as well as massive amplitudes of four-dimensional $mathcalN=4$ SYM on the Coulomb branch.

Full work available at URL: https://arxiv.org/abs/1805.11111

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