Noncommutative deformation of four-dimensional Einstein gravity

Dec, 2002
12 pages
Published in:
  • Class.Quant.Grav. 20 (2003) L95-L104
e-Print:
Report number:
  • IFUM-740-FT

Citations per year

2001200620112016202102468
Abstract:
We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints insure that it is not topological. We find that the choice of the gauge group and of the constraints are crucial to recover a correct deformation of standard gravity. Using the Seiberg-Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve explicitly the constraints and exhibit the first order noncommutative corrections to the Einstein-Hilbert action.
Note:
  • LaTex, 11 pages, comments added, to appear in Classical and Quantum Gravity
  • gravitation
  • differential geometry: noncommutative
  • constraint
  • algebra: Lorentz
  • algebra: Clifford
  • gauge field theory: U(2,2)
  • gauge field theory: SO(1,3)
  • Seiberg-Witten map