Field Equations of Massless Fields in the New Interpretation of the Matrix Model

Abstract

Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the equation of motion of IIB matrix model in this interpretation. In this paper, we generalize this argument to covariant derivatives with torsion. We find that some components of the torsion field can be identified with the dilaton and the $B$-field in string theory. However, the other components do not seem to have string theory counterparts. We also consider the matrix model with a mass term or a cubic term, in which the equation of motion of string theory is exactly satisfied.

arXiv comment21 pages

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• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Factorization of the Effective Action in the IIB Matrix Model
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Quantum gravity equation in large N Yang-Mills quantum mechanics
• Intertwining noncommutativity with gravity and particle physics
• Spherically symmetric solutions of higher-spin gravity in the IKKT matrix model
• Superfield formulation of 4D, N=1 massless higher spin gauge field theory and supermatrix model
• Regularization of matrices in the covariant derivative interpretation of matrix models
• Classical Solutions of a Torsion Gravity from a Large N Matrix Model
• Time and a Temporally Statistical Quantum Geometrodynamics