The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps
Abstract We present new formulas for n-particle tree-level scattering amplitudes of six-dimensional N=11 $$ \mathcal{N}=\left(1,1\right) $$ super Yang-Mills (SYM) and N=22 $$ \mathcal{N}=\left(2,2\right) $$ supergravity (SUGRA). They are written as integrals over the moduli space of certain rational...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2018)125 |
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| author | Freddy Cachazo Alfredo Guevara Matthew Heydeman Sebastian Mizera John H. Schwarz Congkao Wen |
| author_facet | Freddy Cachazo Alfredo Guevara Matthew Heydeman Sebastian Mizera John H. Schwarz Congkao Wen |
| author_sort | Freddy Cachazo |
| collection | DOAJ |
| description | Abstract We present new formulas for n-particle tree-level scattering amplitudes of six-dimensional N=11 $$ \mathcal{N}=\left(1,1\right) $$ super Yang-Mills (SYM) and N=22 $$ \mathcal{N}=\left(2,2\right) $$ 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 N=11 $$ \mathcal{N}=\left(1,1\right) $$ 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 N=22 $$ \mathcal{N}=\left(2,2\right) $$ 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 N=4 $$ \mathcal{N}=4 $$ SYM on the Coulomb branch. |
| first_indexed | 2024-12-20T07:02:44Z |
| format | Article |
| id | doaj.art-5b4cd6eb2ea84d468f478f6ab1e21528 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T07:02:44Z |
| publishDate | 2018-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5b4cd6eb2ea84d468f478f6ab1e215282022-12-21T19:49:10ZengSpringerOpenJournal of High Energy Physics1029-84792018-09-012018918610.1007/JHEP09(2018)125The S matrix of 6D super Yang-Mills and maximal supergravity from rational mapsFreddy Cachazo0Alfredo Guevara1Matthew Heydeman2Sebastian Mizera3John H. Schwarz4Congkao Wen5Perimeter Institute for Theoretical PhysicsPerimeter Institute for Theoretical PhysicsWalter Burke Institute for Theoretical Physics, California Institute of Technology 452-48Perimeter Institute for Theoretical PhysicsWalter Burke Institute for Theoretical Physics, California Institute of Technology 452-48Walter Burke Institute for Theoretical Physics, California Institute of Technology 452-48Abstract We present new formulas for n-particle tree-level scattering amplitudes of six-dimensional N=11 $$ \mathcal{N}=\left(1,1\right) $$ super Yang-Mills (SYM) and N=22 $$ \mathcal{N}=\left(2,2\right) $$ 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 N=11 $$ \mathcal{N}=\left(1,1\right) $$ 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 N=22 $$ \mathcal{N}=\left(2,2\right) $$ 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 N=4 $$ \mathcal{N}=4 $$ SYM on the Coulomb branch.http://link.springer.com/article/10.1007/JHEP09(2018)125Scattering AmplitudesField Theories in Higher DimensionsSupersymmetric Gauge Theory |
| spellingShingle | Freddy Cachazo Alfredo Guevara Matthew Heydeman Sebastian Mizera John H. Schwarz Congkao Wen The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps Journal of High Energy Physics Scattering Amplitudes Field Theories in Higher Dimensions Supersymmetric Gauge Theory |
| title | The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps |
| title_full | The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps |
| title_fullStr | The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps |
| title_full_unstemmed | The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps |
| title_short | The S matrix of 6D super Yang-Mills and maximal supergravity from rational maps |
| title_sort | s matrix of 6d super yang mills and maximal supergravity from rational maps |
| topic | Scattering Amplitudes Field Theories in Higher Dimensions Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP09(2018)125 |
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