Multi-matrix models and emergent geometry

Details Multi-matrix models and emergent geometry Multi-matrix models and emergent geometry

2008-05-30

arxiv.org/abs/0805.4658v2

JHEP 0902:010,2009

Physics

High Energy Physics

High Energy Physics - Theory

1+34 pages, 4 figures. References added

Scientific paper

10.1088/1126-6708/2009/02/010

Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or non-emergence of local geometry at strong coupling is captured by observables that effectively measure the mass of off-diagonal excitations about a semiclassical eigenvalue background. We find emergent geometry at strong coupling in models where a mass term regulates an infrared divergence. We also show that our notion of emergent geometry can be usefully applied to fuzzy spheres. Although most of our results are analytic, we have found numerical input valuable in guiding and checking our results.

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