Curvature and gravity actions for matrix models: II. The case of general Poisson structures

Daniel N Blaschke (1) , Harold Steinacker (1)

1 Faculty of Physics [Vienna]

We study the geometrical meaning of higher-order terms in matrix models of Yang- Mills type in the semi-classical limit, generalizing recent results [ 1 ] 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 ⊂ 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.

Mots clés: Physical Sciences

Daniel N Blaschke, Harold Steinacker. Curvature and gravity actions for matrix models: II. The case of general Poisson structures. Classical and Quantum Gravity, 2010, 27 (23), pp.235019. ⟨10.1088/0264-9381/27/23/235019⟩. ⟨hal-00649077⟩