Built on

S. Lins, “Gems, computers and attractors for 3-manifolds”, Series on Knots and Everything
1974
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F. David, “A model of random surfaces with nontrivial critical behavior”, Nucl. Phys. B
1985
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V. Rivasseau, ”From Perturbative to Constructive Renormalization”, Princeton Series in Physics, 1991. H. Kleinert, V. Schulte-Frohlinde, ”Critical Properties of Φ 4 \Phi^{4} -Theories”, World Scientific Publishing Co Pte Ltd
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D. V. Boulatov, Mod. Phys. Lett. A7
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H. Ooguri, “Topological lattice models in four-dimensions,” Mod. Phys. Lett. A7
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C. Itzykson and J.-B. Zuber, ”Quantum field theory”, McGraw-Hill, 1980. M. Peskins and D. Schroeder, ”An Introduction to Quantum Field Theory”, 1995, Addison-Wesley Advanced Book Program
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R. De Pietri, L. Freidel, K. Krasnov, C. Rovelli, “Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space,” Nucl. Phys. B574
2000
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R. De Pietri, C. Petronio, “Feynman diagrams of generalized matrix models and the associated manifolds in dimension 4,” J. Math. Phys. 41
2000
Earlier work this paper cites.
I. Chepelev, R. Roiban, “Convergence theorem for noncommutative Feynman graphs and renormalization,” JHEP 0103
2001
Earlier work this paper cites.
M. P. Reisenberger, C. Rovelli, “Space-time as a Feynman diagram: The Connection formulation,” Class. Quant. Grav. 18
2003
Earlier work this paper cites.

Similar

D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, “Ultraviolet finite quantum field theory on quantum space-time,” Commun. Math. Phys. 237
2003
Cited alongside, same era.
H. Grosse and R. Wulkenhaar, “Renormalization of phi**4 theory on noncommutative R**4 to all orders,” Lett. Math. Phys. 71
2005
Cited alongside, same era.
R. Oeckl, “Untwisting noncommutative R**d and the equivalence of quantum field theories,” Nucl. Phys. B 581
Original
2007
Cited alongside, same era.
V. Rivasseau, “Non-commutative Renormalization,” Séminaire Henri Poincaré, [arXiv:0705.0705 [hep-th]]. A. Tanasa, “Translation-invariant noncommutative renormalization,” SIGMA 6
Original
2008
Cited alongside, same era.
F. Vignes-Tourneret, “Renormalization of the Orientable Non-commutative Gross-Neveu Model,” Annales Henri Poincare 8

Then

W. T. Tutte, “Graph Theory” , Reading, Mass.: Addison-Wesley, 1984. R. Diestel. “Graph Theory” 2010. Springer-Verlag
2010
Later among the works it cites.
J. Magnen, K. Noui, V. Rivasseau, M. Smerlak,, “Scaling behaviour of three-dimensional group field theory,” Class. Quant. Grav. 26
Original
2010
Later among the works it cites.
J. Ben Geloun, J. Magnen, V. Rivasseau, “Bosonic Colored Group Field Theory,” Eur. Phys. J. C70
Original
2010
Later among the works it cites.
T. Krajewski, J. Magnen, V. Rivasseau, A. Tanasa, P. Vitale, “Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models,” Phys. Rev. D82
Original
2010
Later among the works it cites.
J. Ben Geloun, T. Krajewski, J. Magnen, V. Rivasseau, “Linearized Group Field Theory and Power Counting Theorems,” Class. Quant. Grav. 27

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2011

Multi-orientable Group Field Theory

Tanasa, Adrian

Understand

Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models.

GFT Feynman graphs are tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs are dual not only to manifolds.
In order to simplify the topological structure of these various singularities, colored GFT was recently introduced and intensively studied since.
We propose here a different simplification of GFT, which we call multi-orientable GFT.

Built on

S. Lins, “Gems, computers and attractors for 3-manifolds”, Series on Knots and Everything
1974
Earlier work this paper cites.
F. David, “A model of random surfaces with nontrivial critical behavior”, Nucl. Phys. B
1985
Earlier work this paper cites.
V. Rivasseau, ”From Perturbative to Constructive Renormalization”, Princeton Series in Physics, 1991. H. Kleinert, V. Schulte-Frohlinde, ”Critical Properties of Φ 4 \Phi^{4} -Theories”, World Scientific Publishing Co Pte Ltd
1991
Earlier work this paper cites.
D. V. Boulatov, Mod. Phys. Lett. A7
1992
Earlier work this paper cites.
H. Ooguri, “Topological lattice models in four-dimensions,” Mod. Phys. Lett. A7
1992
Earlier work this paper cites.
C. Itzykson and J.-B. Zuber, ”Quantum field theory”, McGraw-Hill, 1980. M. Peskins and D. Schroeder, ”An Introduction to Quantum Field Theory”, 1995, Addison-Wesley Advanced Book Program
1995
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,” Nucl. Phys. B574
2000
Earlier work this paper cites.
R. De Pietri, C. Petronio, “Feynman diagrams of generalized matrix models and the associated manifolds in dimension 4,” J. Math. Phys. 41
2000
Earlier work this paper cites.
I. Chepelev, R. Roiban, “Convergence theorem for noncommutative Feynman graphs and renormalization,” JHEP 0103
2001
Earlier work this paper cites.
M. P. Reisenberger, C. Rovelli, “Space-time as a Feynman diagram: The Connection formulation,” Class. Quant. Grav. 18
2003
Earlier work this paper cites.

Similar

D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, “Ultraviolet finite quantum field theory on quantum space-time,” Commun. Math. Phys. 237
2003
Cited alongside, same era.
H. Grosse and R. Wulkenhaar, “Renormalization of phi**4 theory on noncommutative R**4 to all orders,” Lett. Math. Phys. 71
2005
Cited alongside, same era.
R. Oeckl, “Untwisting noncommutative R**d and the equivalence of quantum field theories,” Nucl. Phys. B 581
Original
2007
Cited alongside, same era.
V. Rivasseau, “Non-commutative Renormalization,” Séminaire Henri Poincaré, [arXiv:0705.0705 [hep-th]]. A. Tanasa, “Translation-invariant noncommutative renormalization,” SIGMA 6
Original
2008
Cited alongside, same era.
F. Vignes-Tourneret, “Renormalization of the Orientable Non-commutative Gross-Neveu Model,” Annales Henri Poincare 8

Then

W. T. Tutte, “Graph Theory” , Reading, Mass.: Addison-Wesley, 1984. R. Diestel. “Graph Theory” 2010. Springer-Verlag
2010
Later among the works it cites.
J. Magnen, K. Noui, V. Rivasseau, M. Smerlak,, “Scaling behaviour of three-dimensional group field theory,” Class. Quant. Grav. 26
Original
2010
Later among the works it cites.
J. Ben Geloun, J. Magnen, V. Rivasseau, “Bosonic Colored Group Field Theory,” Eur. Phys. J. C70
Original
2010
Later among the works it cites.
T. Krajewski, J. Magnen, V. Rivasseau, A. Tanasa, P. Vitale, “Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models,” Phys. Rev. D82
Original
2010
Later among the works it cites.
J. Ben Geloun, T. Krajewski, J. Magnen, V. Rivasseau, “Linearized Group Field Theory and Power Counting Theorems,” Class. Quant. Grav. 27

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2008

Cited alongside, same era.

G. Schaeffert, Habilitation thesis, 2009, École Polytechnique. G. Chapuy, “Combinatoire bijective des cartes de genre supérieur”, PhD thesis, École Polytechnique (in French)

2009

Cited alongside, same era.

C. Rovelli, “A critical look at strings,” [arXiv:1108.0868 [hep-th]]. C. Rovelli, “A Dialog on quantum gravity,” Int. J. Mod. Phys. D12

Original

2009

Cited alongside, same era.

S. Minwalla, M. Van Raamsdonk, N. Seiberg, “Noncommutative perturbative dynamics,” JHEP 0002

Original

2009

Cited alongside, same era.

L. Freidel, R. Gurau and D. Oriti, “Group field theory renormalization - the 3d case: power counting of divergences,” Phys. Rev. D 80

Original

2009

Cited alongside, same era.

R. Gurau, J. Magnen, V. Rivasseau and A. Tanasa, “A Translation-invariant renormalizable non-commutative scalar model,” Commun. Math. Phys. 287

Original

2009

Cited alongside, same era.

A. Tanasa, “Some combinatorial aspects of quantum field theory,” [arXiv:1102.4231 [math.CO]], submitted

Original

Cited in the paper.

P. Ginsparg, hep-th/9112013. P. di Francesco, “2D quantum gravity, matrix models and graph combinatorics,” NATO Advanced Study Institute, [math-ph/0406013]

Cited in the paper.

Original

2010

Later among the works it cites.

V. Bonzom, M. Smerlak, “Bubble divergences from cellular cohomology,” Lett. Math. Phys. 93

Original

2010

Later among the works it cites.

R. Gurau, “Colored Group Field Theory,” Commun. Math. Phys. 304

Original

2011

Closest in time.