Unified formalism for 6D superamplitudes based on a symplectic Grassmannian

Abstract

Recently, twistor-like formulations of tree amplitudes involving n massless particles have been proposed for various 6D supersymmetric theories. The formulas are based on two different forms of the scattering equations: one based on rational maps and the other based on polarized scattering equations. We show that both formulations can be interpreted in terms of a symplectic (or complex Lagrangian) Grassmannian, LG(n, 2n), and that they correspond to different ways of fixing the GL(n, C) symmetry of LG(n, 2n). This provides an understanding of the equivalence of these different-looking formulas, and it leads to new twistor-like formulas for 6D superamplitudes.

D3-brane loop amplitudes from M5-brane tree amplitudes

“…The tree-level superamplitudes in the M5-brane theory and D5-brane theory are described by twistor formulations either based on rational maps [7][8][9], or based on the polarised scattering equations [10,11] 1 (see also [13] for a recent review on the M5-brane theory and the twistor formulations for the tree-level amplitudes in the theory). These different forms of twistor formulations were later unified in the picture of the Symplectic Grassmannian representation of the 6D superamplitudes [14]. The 6D formulae extend the well-known twistor formulation of the scattering amplitudes for 4D N = 4 super Yang-Mills (SYM) [15,16].…”

“…Analogous constructions for the two-loop amplitudes have been pushed forward in [35][36][37], where two pairs of forward momenta become the loop momenta of the two-loop amplitudes. Instead of using the general dimensional CHY formulations, we will apply the 6D twistor formulations in [7][8][9][10][11]14] to construct loop corrections to amplitudes in 4D. The advantage of using the 6D twistor formulae is that they make the supersymmetry manifest, and allow us to conveniently utilise the spinor-helicity formalism, which is a powerful tool for computing scattering amplitudes in 4D theories (see, for instance, [38,39], for a review.…”

On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring

“…Extrapolating the 6d results of [72,74] one might expect that in 11D spacetime this can be solved in a manner similar to (3.8), Of course, in distinction to 6d and 4d cases, the 11D equations (8.3) (and their 10D counterparts) impose strong constraints on ρ αq (σ) so that their consistency with (8.4) has to be checked. We leave this problem for future work and conclude here by observation that, if this consistency holds, the relation between coefficients of the rational maps and the helicity spinors, encoding the scattering data through (2.2) and (2.11) with (2.5), should be described by 9…”

“…An interesting direction for future study is to apply the spinor frame approach to the construction of 11D and 10D generalization of the 6D rational map and symplectic Grassmannians approach [71,72,73,74]. Its relation to the 6D polarized scattering equation approach of [41] was discussed in very recent [74].…”

Spinor Moving Frame, Polarized Scattering Equation for 11D Supergravity, and Ambitwistor Superstring

“…An interesting direction for future studies is to apply the spinor frame approach to the construction of an 11D generalization of the 6D rational map and symplectic Grassmannian approach [51][52][53][54]. Its relation to the 6D polarized scattering equation approach of [32] was discussed in the very recent work [54].…”