Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure

Abstract

We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4-dimensional space-time geometries with general Poisson structure. Such terms are expected to arise e.g. upon quantization of the IKKT-type models. We identify terms which depend only on the intrinsic geometry and curvature, including modified versions of the Einstein-Hilbert action, as well as terms which depend on the extrinsic curvature. Furthermore, a mechanism is found which implies that the effective metric G on the space-time brane M \subset R^D "almost" coincides with the induced metric g. Deviations from G=g are suppressed, and characterized by the would-be U(1) gauge field.

arXiv comment29 pages; v2 minor update

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• Schwarzschild Geometry Emerging from Matrix Models
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• Thermofield dynamics and Gravity
• Heat kernel expansion and induced action for the matrix model Dirac operator
• On Poisson geometries related to noncommutative emergent gravity
• The curvature of branes, currents and gravity in matrix models
• Phase space quantization, noncommutativity and the gravitational field
• On the geometry of Kähler-Poisson structures
• Special Geometries Emerging from Yang-Mills Type Matrix Models
• Heat kernel expansion and induced action for matrix models