Dynamical phase space from anSO(d,d)matrix model

Abstract

It is shown that a matrix model with SO(d, d) global symmetry is derived from a generalized Yang-Mills theory on the standard Courant algebroid. This model keeps all the positive features of the well-studied type IIB matrix model, and it has many additional welcome properties. We show that it does not only capture the dynamics of spacetime, but it should be associated with the dynamics of phase space. This is supported by a large set of classical solutions of its equations of motion, which corresponds to phase spaces of noncommutative curved manifolds and points to a new mechanism of emergent gravity. The model possesses a symmetry that exchanges positions and momenta, in analogy to quantum mechanics. It is argued that the emergence of phase space in the model is an essential feature for the investigation of the precise relation of matrix models to string theory and quantum gravity.PACS numbers: 02.40Gh, 04.60.-m, 11.10Kk, 11.25Sq.The concept of spacetime at very short distance scales is very different than in classical physics. Ultimately, classical spacetime and the gravitational field of general relativity are expected to be emergent concepts. The most prominent physical framework where this is indeed the case is perturbative string theory, where the starting point is an extended degree of freedom described by a non-linear sigma model. The perturbative quantization of the theory indeed reveals the presence of gravity. In a rather independent way, matrix theories [1-3] should also have something to say about quantum gravity, although the situation in this line of research remains more unclear. The emergence of gravity in matrix models is an interesting problem to address (see Ref.[4] and its references for a review of some approaches), especially since the models of Refs. [1-3] are conjectured to be directly related to string theory and to capture its nonperturbative dynamics.On the other hand, it is reasonable to think that understanding the structure of spacetime at high energies is just part of the story. When quantum-mechanical effects become important, it can be argued that it is the structure of full phase space and its dynamics that would provide a more complete understanding of quantum gravity. This was emphasized recently from the point of view of string theory in Refs. [5,6] and earlier from the point of view of noncommutative geometry in Refs. [7][8][9]. Given the close relation of string theory and noncommutative geometry [10,11] and their common grounds with matrix models, it is interesting to examine whether the dynamics of phase space can be captured by a matrix model. In this letter we suggest such a model. We show that starting with a generalized connection on the standard Courant algebroid we can define a Yang-Mills (YM) theory whose reduction to a point yields a matrix model with additional degrees of freedom and SO(d, d) global symmetry. The symetries of this matrix model dictate that the classical solutions of its equations of motion (EOMs) are noncommutative phase space algebras that inc...

A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

“…(See Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] for related works.) It was also suggested from Monte Carlo simulation of simplified models that the expansion is exponential at the beginning and it turns into a power law at late times [5,6].…”

Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

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