The Chern-Simons One-form and Gravity on a Fuzzy Space

Abstract

The one-dimensional $\mathcal{N}\times \mathcal{N}$-matrix Chern-Simons action is given, for large $\mathcal{N}$ and for slowly varying fields, by the $(2k+1)$-dimensional Chern-Simons action $S_{CS}$, where the gauge fields in $S_{CS}$ parametrize the different ways in which the large $\mathcal{N}$ limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chern-Simons action at finite $\mathcal{N}$ and by the higher dimensional Chern-Simons action when the fuzzy space is approximated by a continuous manifold.

16 pages, references added

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Cited by in corpus (11)

• Symmetry, Gravity and Noncommutativity
• Emergent Gravity from Noncommutative Gauge Theory
• Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert lagrangian
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Inherent Holography In Fuzzy Spaces and An N-tropic Approach To The Cosmological Constant Problem
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Thermofield dynamics and Gravity
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Intertwining noncommutativity with gravity and particle physics
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields