Curvature and Gravity Actions for Matrix Models

Abstract

We show how gravitational actions, in particular the Einstein-Hilbert action, can be obtained from additional terms in Yang-Mills matrix models. This is consistent with recent results on induced gravitational actions in these matrix models, realizing space-time as 4-dimensional brane solutions. It opens up the possibility for a controlled non-perturbative description of gravity through simple matrix models, with interesting perspectives for the problem of vacuum energy. The relation with UV/IR mixing and non-commutative gauge theory is discussed.

17 pages; v2+v3: minor corrections

References in corpus (4)

• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• Emergent Gravity, Matrix Models and UV/IR Mixing
• Orbifolds, fuzzy spheres and chiral fermions
• Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions

Cited by in corpus (13)

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• On the 1-loop effective action for the IKKT model and non-commutative branes
• Schwarzschild Geometry Emerging from Matrix Models
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Thermofield dynamics and Gravity
• On Poisson geometries related to noncommutative emergent gravity
• Heat kernel expansion and induced action for the matrix model Dirac operator
• Pseudo-Riemannian geometry in terms of multi-linear brackets
• Cosmic acceleration in Regge-Teitelboim gravity
• Dark Energy from the Fifth Dimension
• Phase space quantization, noncommutativity and the gravitational field
• Curvature and geometric modules of noncommutative spheres and tori
• Heat kernel expansion and induced action for matrix models