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

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

2010-07-16

arxiv.org/abs/1007.2729v2

Class.Quant.Grav.27:235019,2010

Physics

High Energy Physics

High Energy Physics - Theory

29 pages; v2 minor update

Scientific paper

10.1088/0264-9381/27/23/235019

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.

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