Spinor moving frame, type II superparticle quantization, hidden $SU(8)$ symmetry of linearized 10D supergravity, and superamplitudes

Abstract: A covariant quantization of type IIB and type IIA superparticles in their spinor moving frame formulation reveals the hidden $SU(8)$ symmetry of the linearized type II supergravity. It acts on auxiliary variables parameterizing the possible choices of complex structures which is necessary to arrive at the realization of the quantum state vector as an analytic on-shell superfield, the one-particle counterpart of analytical superamplitudes for type IIB and type IIA supergravity multiplets. The description of the type IIA supergraity multiplet in terms of an analytic on-shell superfield is then identical to that for type IIB supermultiplet; the difference is in spacetime interpretation. However, the definition of suitable auxiliary variables in type IIA case requires introduction of covariantly constant $SO(8)$ vector which can be related to T-duality transform between type IIA and type IIB superspaces. The simplest analytic IIB superamplitudes discussed in the literature thus also describe type IIA processes. We elaborate on these using the spinor moving frame (Lorentz harmonic) formalism and point out the restrictions on computation of many particle type IIA amplitudes in this approach. We also briefly discuss the initial steps towards type IIA superamplitudes involving, besides supergravity multiplets, also D$0$-branes (Dirichlet superparticles), which was recently quantized in the similar formalism, and indicate some problems which appear are to be solved to proceed on this way.