SO(9, 1) invariant matrix formulation of a supermembrane Original Research Article

n SO(9, 1) invariant formulation of an 11-dimensional supermembrane is presented by combining an SO(10, 1) invariant treatment of reparametrization symmetry with an SO(9, 1) invariant θR = 0 gauge of κ-symmetry. The Lagrangian thus defined consists of polynomials in dynamical variables (up to quartic terms in Xμ and up to the eighth power in θ), and reparametrization BRST symmetry is manifest. The area preserving diffeomorphism is consistently incorporated and the area preserving gauge symmetry is made explicit. The SO(9, 1) invariant theory contains terms which cannot be induced by a naive dimensional reduction of higher-dimensional supersymmetric Yang-Mills theory. The SO(9, 1) invariant Hamiltonian and the generator of area preserving diffeomorphism together with the supercharge are matrix regularized by applying the standard procedure. As an application of the present formulation, we evaluate the possible central charges in superalgebra both in the path integral and in the canonical (Dirac) formalism, and we find only the two-form charge [Xμ, Xν].