Matsuo Sato

COVARIANT FORMULATION OF M-THEORY

We propose the bosonic part of an action that defines M-theory. It possesses manifest SO(1, 10) symmetry and constructed based on the Lorentzian 3-algebra associated with U(N) Lie algebra. From our action, we derive the bosonic sector of BFSS matrix theory and IIB matrix model in the naive large N limit by taking appropriate vacua. We also discuss an interaction with fermions.

Model of M-theory with eleven matrices

We show that an action of a supermembrane in an eleven-dimensional spacetime with a semi-light-cone gauge can be written only with Nambu-Poisson bracket and an invariant symmetric bilinear form under an approximation. Thus, the action under the conditions is manifestly covariant under volume preserving diffeomorphism even when the world-volume metric is flat. Next, we propose two 3-algebraic models of M-theory which are obtained as a second quantization of an action that is equivalent to the supermembrane action under the approximation. The second quantization is defined by replacing Nambu-Poisson bracket with finite-dimensional 3-algebras’ brackets. Our models include eleven matrices corresponding to all the eleven space-time coordinates in M-theory although they possess not SO(1, 10) but SO(1, 2) × SO(8) or SO(1, 2) × SU(4) × U(1) covariance. They possess

Zariski quantization as second quantization

\mathcal{N} = 1

Extension of IIB Matrix Model by Three-Algebra

space-time supersymmetry in eleven dimensions that consists of 16 kinematical and 16 dynamical ones. We also show that the SU(4) model with a certain algebra reduces to BFSS matrix theory if DLCQ limit is taken.

BPS BOUND STATES OF D6-BRANES AND LOWER-DIMENSIONAL D-BRANES

In M. Sato, J. High Energy Phys. 07 (2010) 026, we proposed two models of M theory, the Hermitian 3-algebra model and Lie 3-algebra model. In this paper, we study the Lie 3-algebra model with a Lorentzian Lie 3-algebra. This model is ghost-free despite the Lorentzian 3-algebra. We show that our model satisfies two criteria as a model of M theory. First, we show that the model possesses

Four-algebraic extension of the IIB matrix model

\mathcal{N}=1

Hermitian generalized Jordan triple systems and certain applications to field theory

supersymmetry in 11 dimensions. Second, we show the model reduces to Banks-Fischler-Shenker-Susskind matrix theory with finite size matrices in a discrete light-cone quantization limit.

On the structure constants of volume preserving diffeomorphism algebra

The Zariski quantization is one of the strong candidates for a quantization of the Nambu-Poisson bracket. In this paper, we apply the Zariski quantization for first quantized field theories, such as superstring and supermembrane theories, and clarify physical meaning of the Zariski quantization. The first quantized field theories need not to possess the Nambu-Poisson structure. First, we construct a natural metric for the spaces on which Zariski product acts in order to apply the Zariski quantization for field theories. This metric is invariant under a gauge transformation generated by the Zariski quantized Nambu-Poisson bracket. Second, we perform the Zariski quantization of superstring and supermembrane theories as examples. We find flat directions, which indicate that the Zariski quantized theories describe many-body systems. We also find that pair creations and annihilations occur among the many bodies introduced by the Zariski quantization, by studying a simple model. These facts imply that the Zariski quantization is a second quantization. Moreover, the Zariski quantization preserves supersymmetries of the first quantized field theories. Thus, we can obtain second quantized theories of superstring and supermembranes by performing the Zariski quantization of the superstring and supermembrane theories.