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• W3102880415 abstract "A bstract We present new formulas for n -particle tree-level scattering amplitudes of six-dimensional $$ mathcal{N}=left(1,1right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mn>1</mml:mn> </mml:mfenced> </mml:math> super Yang-Mills (SYM) and $$ mathcal{N}=left(2,2right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>2</mml:mn> <mml:mn>2</mml:mn> </mml:mfenced> </mml:math> 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 $$ mathcal{N}=left(1,1right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mn>1</mml:mn> </mml:mfenced> </mml:math> 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 SL(2 , ℂ) 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 $$ mathcal{N}=left(2,2right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>2</mml:mn> <mml:mn>2</mml:mn> </mml:mfenced> </mml:math> 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 $$ mathcal{N}=4 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> SYM on the Coulomb branch." @default.
• W3102880415 created "2020-11-23" @default.
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• W3102880415 date "2018-09-01" @default.
• W3102880415 modified "2023-10-14" @default.
• W3102880415 title "The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps" @default.
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• W3102880415 doi "https://doi.org/10.1007/jhep09(2018)125" @default.
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