Covariant Matrix Model of Superparticle in the 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.

13 pages, no figures, two references added

References in corpus (2)

• The Superembedding Origin of the Berkovits Pure Spinor Covariant Quantization of Superstrings
• Correlation Functions in Berkovits' Pure Spinor Formulation

Cited by in corpus (6)

• Origin of Pure Spinor Superstring
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• Relating Green-Schwarz and Extended Pure Spinor Formalisms by Similarity Transformation
• Operator Mapping between RNS and Extended Pure Spinor Formalisms for Superstring
• Worldline Approach of Topological BF Theory
• Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --