Quantum state spectrum and field theory of D$0$-brane

TL;DR

This work covariantly quantizes a single D0-brane in the spinor moving frame, deriving its Hamiltonian structure and showing that the quantum state is encoded in an on-shell chiral superfield. The authors identify the spectrum with the massive counterpart of linearized Type IIA supergravity, realized as the next KK mode from 11D supergravity, and they explicitly construct the corresponding fermionic and bosonic fields in SO(9) and SO(7) covariant forms. By solving the linearized massive field equations and matching them to the superfield components, they establish a one-to-one correspondence between the quantum states and the 10D massive Type IIA multiplet, including its gauge and supersymmetry structure. The results provide a solid basis for quantizing the full mD0 action and hint at hidden SU(8) symmetry and spinor-helicity approaches, with potential impact on Type IIA amplitudes and higher-dimensional holographic frameworks.

Abstract

We quantize D$0$-brane, the simplest representative of the family of supersymmetric Dirichlet p-branes, in its spinor moving frame formulation and analyze its quantum state spectrum. Besides being a preparatory stage for quantization of the complete supersymmetric multiple D$0$-brane (mD$0$) model, which is presently known only in the frame of spinor moving frame formalism, this is interesting as its own: despite the covariant quantization of D=10 D$0$-brane was discussed before, its quantum state spectrum was not analyzed and its field theory, describing that, was not studied. We show that the quantum state vector of the D$0$-brane is described by an on-shell superfield that collects the fields of the massive counterpart of the linearized type IIA supergravity supermultiplet which can be obtained as massive Kaluza-Klein mode of the dimensional reduction of the eleven dimensional supergravity down to ten dimensions. In conclusion, we briefly discuss a spinor helicity formalism for D$0$-brane which can be used as one of the basic elements for developing type IIA string theory amplitude calculus based on multiparticle generalizations of the on-shell superfields.