Gravity and compactified branes in matrix models

Abstract

A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor θ^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are transmitted to the 4 noncompact directions via the Poisson tensor. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it might provide a way to avoid the landscape problem in string theory.

35 pages. V2: substantially revised and improved, conclusion weakened. V3: some clarifications, published version. V4: minor correction

References in corpus (7)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions
• Spontaneous Symmetry Probing
• Cosmological solutions of emergent noncommutative gravity
• On the 1-loop effective action for the IKKT model and non-commutative branes
• Instantons, Twistors, and Emergent Gravity
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure

Cited by in corpus (11)

• Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model
• 2D fuzzy Anti-de Sitter space from matrix models
• Emergent gravity on covariant quantum spaces in the IKKT model
• Multi-matrix models at general coupling
• On the Phase Structure of Commuting Matrix Models
• Near commuting multi-matrix models
• Brane compactifications and 4-dimensional geometry in the IKKT model
• One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
• Dirac equation on coordinate dependent noncommutative space-time
• The curvature of branes, currents and gravity in matrix models
• Influences of the coordinate dependent noncommutative space on charged and spin currents