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A Deformed Poincare Invariance for Group Field Theories · Around

2010

A Deformed Poincare Invariance for Group Field Theories

Girelli, Florian, Livine, Etera R.

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In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams.

They can be understood as generalizations of the matrix models used for 2d quantum gravity.
In particular Boulatov's theory reproduces the amplitudes of the Ponzano-Regge spinfoam model for 3d quantum gravity.
Motivated by recent works on field theories on non-commutative flat spaces, we show that Boulatov's theory (and its colored version) is actually invariant under a global deformed Poincare symmetry.

Built on

R. Gurau, Topological Graph Polynomials in Colored Group Field Theory
Original
1945
Earlier work this paper cites.
D. Boulatov, A Model of Three-Dimensional Lattice Gravity
1992
Earlier work this paper cites.
H. Ooguri, Topological Lattice Models in Four Dimensions
1992
Earlier work this paper cites.
C. Rovelli, The basis of the Ponzano-Regge-Turaev-Viro-Ooguri model is the loop representation basis
1993
Earlier work this paper cites.
M.P. Reisenberger, C. Rovelli, “Sum over Surfaces” form of Loop Quantum Gravity
1997
Earlier work this paper cites.
J.C. Baez, Spin Foam Models
1998
Earlier work this paper cites.
R. De Pietri, L. Freidel, K. Krasnov, C. Rovelli, Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
2000
Earlier work this paper cites.

Similar

M.P. Reisenberger, C. Rovelli, Spacetime as a Feynman diagram: the connection formulation
2001
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L. Freidel, D. Louapre, Non-perturbative summation over 3D discrete topologies
2003
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L. Freidel, D. Louapre, Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
2004
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L. Freidel, Group Field Theory: An overview
2005
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L. Freidel, E.R. Livine, 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
2006
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W. Fairbairn, E.R. Livine, 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
2007

Then

L. Freidel, R. Gurau, D. Oriti, Group field theory renormalization - the 3d case: power counting of divergences
Original
2009
Later among the works it cites.
J. Magnen, K. Noui, V. Rivasseau, M. Smerlak, Scaling behaviour of three-dimensional group field theory
Original
2009
Later among the works it cites.
E. Joung, J. Mourad, K. Noui, Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
Original
2009
Later among the works it cites.
E.R. Livine, Matrix Models as Non-commutative Field Theories on ℝ 3 {\mathbb{R}}^{3}
Original
2009
Later among the works it cites.
E.R. Livine, J.P. Ryan, A Note on B-observables in Ponzano-Regge 3d Quantum Gravity
Original

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