Wilson loops, geometric operators and fermions in 3d group field theory

R. Dowdall 1
  • 1 University of Nottingham, Nottingham, UK

Abstract

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler “quenched” approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO9780511755804

  • [2] D. Oriti, arXiv:gr-qc/0607032

  • [3] L. Freidel, Int. J. Theor. Phys. 44, 1769 (2005) http://dx.doi.org/10.1007/s10773-005-8894-1

  • [4] L. Freidel, D. Louapre, Classical Quant. Grav. 21, 5685 (2004) http://dx.doi.org/10.1088/0264-9381/21/24/002

  • [5] W.J. Fairbairn, A. Perez, Phys. Rev. D 78, 024013 (2008) http://dx.doi.org/10.1103/PhysRevD.78.024013

  • [6] L. Freidel, E.R. Livine, Classical Quant. Grav. 23, 2021 (2006) http://dx.doi.org/10.1088/0264-9381/23/6/012

  • [7] D. Oriti, J. Ryan, Classical Quant. Grav. 23, 6543 (2006) http://dx.doi.org/10.1088/0264-9381/23/22/027

  • [8] W.J. Fairbairn, E.R. Livine, Classical Quant. Grav. 24, 5277 (2007) http://dx.doi.org/10.1088/0264-9381/24/20/021

  • [9] W.J. Fairbairn, Gen. Rel. Gravit. 39, 427 (2007) http://dx.doi.org/10.1007/s10714-006-0395-x

  • [10] L. Freidel, D. Louapre, arXiv:gr-qc/0410141

  • [11] D.V. Boulatov, Mod. Phys. Lett. A 7, 1629 (1992) http://dx.doi.org/10.1142/S0217732392001324

  • [12] L. Freidel, K. Krasnov, Adv. Theor. Math. Phys. 2, 1183 (1999)

  • [13] J. Hackett, S. Speziale, Classical Quant. Grav. 24, 1525 (2007) http://dx.doi.org/10.1088/0264-9381/24/6/010

  • [14] D. Oriti, T. Tlas, Classical Quant. Grav. 25, 085011 (2008) http://dx.doi.org/10.1088/0264-9381/25/8/085011

  • [15] R. Gurau, arXiv:0907.2582v1 [hep-th]

OPEN ACCESS

Journal + Issues

Search