2D fuzzy anti-de Sitter space from matrix models
- 227 Downloads
We study the fuzzy hyperboloids AdS2 and dS2 as brane solutions in matrix models. The unitary representations of SO(2, 1) required for quantum field theory are identified, and explicit formulae for their realization in terms of fuzzy wavefunctions are given. In a second part, we study the (A)dS2 brane geometry and its dynamics, as governed by a suitable matrix model. In particular, we show that trace of the energy-momentum tensor of matter induces transversal perturbations of the brane and of the Ricci scalar. This leads to a linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism of emergent gravity in matrix models.
KeywordsNon-Commutative Geometry M(atrix) Theories 2D Gravity
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- H. Miglbauer, Kovariante nichtkommutative Näherungen nichtkompakter Geometrien und Nicht-Euklidische 2D-Fuzzy-Quantenfelder, PhD thesis, Technical University Graz, 1994, unpublished.Google Scholar
- S. Waldmann, Poisson-Geometrie und Deformations-quantisierung, Springer, 2007.Google Scholar
- J. Arnlind, J. Choe and J. Hoppe, Noncommutative Minimal Surfaces, arXiv:1301.0757.