Abstract
Tree amplitudes of 10D supersymmetric Yang-Mills theory (SYM) and 11D supergravity (SUGRA) are collected in multi-particle counterparts of analytic on-shell superfields. These have essentially the same form as their chiral 4D counterparts describing mathcal{N}=4 SYM and mathcal{N}=8 SUGRA, but with components dependent on a different set of bosonic variables. These are the D=10 and D=11 spinor helicity variables, the set of which includes the spinor frame variable (Lorentz harmonics) and a scalar density, and generalized homogeneous coordinates of the coset frac{mathrm{SO}left(D-2right)}{mathrm{SO}left(D-4right)otimes mathrm{U}(1)} (internal harmonics).We present an especially convenient parametrization of the spinor harmonics (Lorentz covariant gauge fixed with the use of an auxiliary gauge symmetry) and use this to find (a gauge fixed version of) the 3-point tree superamplitudes of 10D SYM and 11D SUGRA which generalize the 4 dimensional anti-MHV superamplitudes.
Highlights
An impressive recent progress in calculation of multi-loop amplitudes of d=4 supersymmetric Yang-Mills (SYM) and supergravity (SUGRA) theories, especially of their maximally supersymmetric versions N = 4 supersymmetric Yang-Mills theory (SYM) and N = 8 SUGRA [1,2,3,4,5], was reached in its significant part with the use of spinor helicity formalism and of its superfield generalization [6, 7, 9,10,11,12,13]
We present an especially convenient parametrization of the spinor harmonics (Lorentz covariant gauge fixed with the use of an auxiliary gauge symmetry) and use this to find the 3-point tree superamplitudes of 10D SYM and 11D SUGRA
We show how the analytic superamplitudes are constructed from the basic constrained superamplitudes of 10D SYM and 11D SUGRA and the set of complex (D − 2) component null-vectors UI i related to the internal frame associated to i-th scattered particle
Summary
An alternative, constrained superfield formalism was proposed for 11D SUGRA amplitudes in [15]; its 10D SYM cousin will be briefly described here (see [31] and [16] for details) In it the superamplitudes carry the indices of ‘little groups’ SO(D − 2)i of the light-like momenta ka(i) of i-th scattered particles and obey a set of differential equations involving fermionic covariant derivatives Dq+(i). Appendix B shows how to obtain the BCFW-like deformation of the 10/11D spinor helicity and complex fermionic variables from the deformation of real spinor frame and real fermionic variables found in [14, 15]
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