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

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.Comment: 29 pages; v2 minor updat

Compactified rotating branes in the matrix model, and excitation spectrum towards one loop

We study compactified brane solutions of type R^4 x K in the IIB matrix model, and obtain explicitly the bosonic and fermionic fluctuation spectrum required to compute the one-loop effective action. We verify that the one-loop contributions are UV finite for R^4 x T^2, and supersymmetric for R^3 x S^1. The higher Kaluza-Klein modes are shown to have a gap in the presence of flux on T^2, and potential problems concerning stability are discussed.Comment: 14 pages, 1 figure; v2 typos correcte