Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity

Abstract

We show that 10D spinor helicity formalism can be understood as spinor moving frame approach to supersymmetric particles extended to the description of amplitudes. This allows us to develop the spinor helicity formalism for 11D supergravity and a new constrained superfield formalism for 10D SYM and 11D SUGRA amplitudes. We show how the constrained on-shell superfields, one-particle counterparts of the superamplitudes, can be obtained by quantization of massless superparticle mechanics. We make some stages towards the calculation of amplitudes of 10D SYM and 11D SUGRA in this framework. In particular we have found supersymmetric Ward identities for constrained amplitudes and an especially convenient gauge, fixed on the spinor frame variables corresponding to scattered particles, which promises to be an extremely useful tool for further development of our approach. We also discuss a candidate for generalization of the BCFW recurrent relations for the constrained tree superamplitudes, indicate and discuss a problem of dependence of the expressions obtained with it on a deformation vector, which is not fixed uniquely in higher dimensional D > 4 cases.variables; this fact does not diminish the significance of these which were used quite extensively in [18].2 Also a momentum twistor formalism, alternative (dual) to the standard twistor approach and related to dual superconformal symmetry [9], rather than to the standard conformal symmetry of N = 4 SYM, was developed in [22,23]. 3 The identification of spinor helicity variables with Lorentz harmonics were noticed in [33] and used there to construct D=5 spinor helicity formalism. 4 The spinor moving frame approach for D=4 and D=10 superstrings was proposed in [38] and elaborated in [39], for 11D supermembrane in [40] and for the generic super-p-branes from the 'standard brane scan ' -in [41]. The synthesis of spinor moving frame approach with the so-called STV (Sorokin-Tkach-Volkov) approach to superparticles and superstrings [42,43,44] (see [45] for the review and more references) resulted in the development of the superembedding approach to superstrings and super-p-branes [46]. In particular, in the frame of this approach (also reviewed in [45]) the equations of motion of the M-theory 5-brane had been obtained in [47] some months before the covariant actions was constructed in [48] and [49].

Spinor-Helicity Formalism for Massless Fields in AdS4

“…For review on modern amplitude methods and on the spinor-helicity formalism, see [2][3][4]. The success of the spinor-helicity formalism for theories of massless particles in four dimensions motivated its various extensions -to other dimensions [5][6][7][8][9] and to massive fields [10][11][12][13].Another line of research that lead to important developments in recent years is the AdS/CFT correspondence. It is a conjectured duality between gravitational theories in AdS space and conformal theories on its boundary [14][15][16].…”

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

“…and to adapt it to our light-like momentum k µi by assuming that one of its light-like vectors, say u = µi = u 0 µi − u 10 µi , is proportional to k µi (see [52,27] and refs. therein, in particular [57,58])…”

“…The development of this twisor-like formalism for the case of higher dimensional theories and its applications were discussed in [19,20,21,22,23,24,25,26,27,28]. In particular, in [25,27] the observation that 10D spinor helicity formalism of [20] can be understood as spinor moving frame approach to supersymmetric particles extended to the description of amplitudes 1 allowed us to develop the spinor helicity formalism for 11D supergravity and a new constrained superfield formalism for 10D SYM and 11D SUGRA amplitudes, to find the Ward identities for these amplitudes and to discuss a candidate for generalization of the BCFW recurrent relations [12] for the constrained tree superamplitudes. In [26] an alternative analytic superfield formalism for superamplitudes was proposed.…”

“…3, after reviewing the scattering equation [35] (sec. 3.1), we revisit the 11D polarized scattering equation of [28] with the use of the spinor frame version of the spinor helicity formalism [25,26,27]. In sec.…”

“…Our notation are that of [25,27] and [26], up to the use of underlined Greek symbols from the beginning/middle of the alphabet for the 11D Majorana spinors/vectors and underlined Latin indices from the SO(9) vector (I, J, ...) and spinor indices (q, p, ...). In some places q, p, ... are also considered to be SO(16) vector indices which is related to the hidden SO(16) symmetry of 11D superparticle (see [52] and refs.…”