Covariant Matrix Model of Superparticle in the Pure Spinor Formalism

TL;DR

This paper constructs a covariant and supersymmetric matrix model of the 11D superparticle based on the pure spinor formalism, demonstrating its trivial one-loop effective potential and suggesting it is a free theory.

Contribution

It introduces a covariant, supersymmetric matrix model of the 11D superparticle derived from the pure spinor formalism, addressing challenges in covariant supermembrane M(atrix) theories.

Findings

One-loop effective potential is trivial.

The matrix model is a free theory at one-loop level.

Constructs a covariant superparticle matrix model from pure spinor formalism.

Abstract

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under $SO(1,10)$ Lorentz group. We first construct a bosonic M(atrix) theory by starting with the first-order formalism of bosonic membrane, which precisely gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this method to the construction of M(atrix) theory of supermembranes. However, it seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory from the Berkovits pure spinor formalism of supermembrane because of the matrix character of the BRST symmetry. Instead, in this paper, we construct a supersymmetric and covariant matrix model of 11D superparticle, which corresponds to a particle limit of covariant M(atrix) theory. By an explicit calculation, we show that the one-loop effective potential is trivial, thereby implying that this matrix model is a free theory at least at the one-loop level.