Symmetries, Matrices, and de Sitter Gravity

Abstract

Using simple algebraic methods along with an analogy to the BFSS model, we explore the possible (target) spacetime symmetries that may appear in a matrix description of de Sitter gravity. Such symmetry groups could arise in two ways, one from an ``IMF'' like construction and the other from a ``DLCQ'' like construction. In contrast to the flat space case, we show that the two constructions will lead to different groups, i.e. the Newton-Hooke group and the inhomogeneous Euclidean group (or its algebraic cousins). It is argued that matrix quantum mechanics based on the former symmetries look more plausible. Then, after giving a detailed description of the relevant one particle dynamics, a concrete Newton-Hooke matrix model is proposed. The model naturally incorporates issues such as holography, UV-IR relations, and fuzziness, for gravity in $d{S}_4$. We also provide evidence to support a possible phase transition. The lower temperature phase, which corresponds to gravity in the perturbative regime, has a Hilbert space of infinite dimension. In the higher temperature phase where the perturbation theory breaks down, the dimension of the Hilbert space may become finite.

38 pages, no figures

References in corpus (4)

• The dS/CFT Correspondence
• Deconstructing de Sitter
• Conformal anomaly from dS/CFT correspondence
• Matrix Model for De Sitter

Cited by in corpus (11)

• Conformal mechanics in Newton-Hooke spacetime
• Dynamical realizations of l-conformal Newton-Hooke group
• Matrix Cosmology
• Cardy-Verlinde Formula and Achucarro-Ortiz Black Hole
• Zero-Branes, Quantum Mechanics and the Cosmological Constant
• Orbifold Physics and de Sitter Spacetime
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• The Non-Relativistic Superparticle in a Curved Background
• Three-dimensional non-relativistic supergravity and torsion
• Supermatrix models for M-theory based on osp(1|32,R)
• Higher-derivative superparticle in AdS${}_3$ space