Eleven dimensional supergravity in light cone gauge

Light-cone gauge manifestly supersymmetric formulation of 11 dimensional supergravity is developed. The formulation is given entirely in terms of light-cone scalar superfield, allowing us to treat all component fields on an equal footing. All higher derivative on mass-shell manifestly supersymmetric $4$-point functions invariant with respect to linear supersymmetry transformations and corresponding (in gravitational bosonic sector) to terms constructed from four Riemann tensors and derivatives are found. Superspace representation for $4$-point scattering amplitudes is also obtained. Superfield representation of linearized interaction vertex of superparticle and supergravity fields is presented. All $4$-point higher derivative interaction vertices of ten-dimensional supersymmetric Yang-Mills theory are also determined.