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.
Keywords
Cite
@article{arxiv.1007.2729,
title = {Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure},
author = {Daniel N. Blaschke and Harold Steinacker},
journal= {arXiv preprint arXiv:1007.2729},
year = {2011}
}
Comments
29 pages; v2 minor update