An analytic superfield formalism for tree superamplitudes in D=10 and D=11

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 N = 4 SYM and 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 SO(D−2) SO(D−4)⊗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.

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

“…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 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. It was also oriented on the use of BCFW-type recurrent relations which are still to be found in this case.…”

“…We begin in sec. 2 by reviewing the spinor frame description of the 11D spinor helicity formalism [26]. In sec.…”

“…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.…”