Emergent Gravity from Noncommutative Gauge Theory

Abstract

We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric G_{ab}, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. This leads to a class of metrics which contains the physical degrees of freedom of gravitational waves, and allows to recover e.g. the Newtonian limit with arbitrary mass distribution. It also suggests a consistent picture of UV/IR mixing in terms of an induced gravity action. This should provide a suitable framework for quantizing gravity.

28 pages + 11 pages appendix. V2: references and discussion added. V3: minor correction

References in corpus (15)

• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• Induced Gauge Theory on a Noncommutative Space
• A note on the noncommutative correction to gravity
• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• Lie algebraic Noncommutative Gravity
• Fermions on spontaneously generated spherical extra dimensions
• On The Correspondence Between Noncommuative Field Theory And Gravity
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Noncommutative Electromagnetism As A Large N Gauge Theory
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Graviton Propagators in Supergravity and Noncommutative Gauge Theory
• Perturbative Vacua from IIB Matrix Model
• Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2

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