Topological graph polynomials in colored group field theory

Annales Henri Poincare

Volumn 11, Issue 4, 2010, Pages 565-584

  Gurau, Razvan ^a  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955558767     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-010-0035-6     Document Type: Article

References (50)

1. Gurau, R.: Colored group field theory. arXiv: 0907. 2582 [hep-th].
2. Nakanishi N.: Graph Theory and Feynman Integrals. Gordon and Breach, New York (1970).
3. Itzykson C., Zuber J.-B.: Quantum Field Theory. McGraw and Hill, New York (1980).
4. David F.: A model of random surfaces with nontrivial critical behavior. Nucl. Phys. B 257, 543 (1985).
5. Ginsparg, P.: Matrix models of 2-d gravity. arXiv: hep-th/9112013.
6. Gross M.: Tensor models and simplicial quantum gravity in > 2-D. Nucl. Phys. Proc. Suppl. 25A, 144-149 (1992).
7. Sasakura N.: Tensor model for gravity and orientability of manifold. Mod. Phys. Lett. A 6, 2613 (1991).
8. Connes A.: Noncommutative Geometry. Academic Press Inc., San Diego (1994).
9. Douglas M. R., Nekrasov N. A.: Noncommutative field theory. Rev. Mod. Phys. 73, 977 (2001) arXiv: hep-th/0106048.
10. 4 in the matrix base. Commun. Math. Phys. 256(2), 305 (2005) arXiv: hep-th/0401128.
11. Grosse H., Wulkenhaar R.: Power-counting theorem for non-local matrix models and renormalization. Commun. Math. Phys. 254(1), 91 (2005) arXiv: hep-th/0305066.
12. 4-theory by multi-scale analysis. Commun. Math. Phys. 262, 565 (2006) arXiv: hep-th/0501036.
13. 4 field theory in x space. Commun. Math. Phys. 267(2), 515 (2006) arXiv: hep-th/0512271.
14. Gurau R., Magnen J., Rivasseau V., Tanasa A.: A translation-invariant renormalizable non-commutative scalar model. Commun. Math. Phys. 287, 275 (2009) arXiv: 0802. 0791 [math-ph].
15. 't Hooft G.: A planar diagram theory for strong interactions. Nucl. Phys. B 72, 461 (1974).
16. 4-theory. Eur. Phys. J. C35, 277 (2004) arXiv: hep-th/0402093.
17. Disertori M., Rivasseau V.: Two and three loops beta function of non commutative phi(4)**4 theory. Eur. Phys. J. C 50, 661 (2007) arXiv: hep-th/0610224.
18. Disertori M., Gurau R., Magnen J., Rivasseau V.: Vanishing of beta function of non commutative phi(4)**4 theory to all orders. Phys. Lett. B 649, 95 (2007) arXiv: hep-th/0612251.
19. Gurau R., Rosten O. J.: Wilsonian renormalization of noncommutative scalar field theory. JHEP 0907, 064 (2009) arXiv: 0902. 4888 [hep-th].
20. Geloun J. B., Gurau R., Rivasseau V.: Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field. Phys. Lett. B 671, 284 (2009) arXiv: 0805. 4362 [hep-th].
21. Boulatov D.: A model of three-dimensional lattice gravity. Mod. Phys. Lett. A 7, 1629-1646 (1992) arXiv: hep-th/9202074.
22. Freidel L.: Group field theory: an overview. Int. J. Phys. 44, 1769-1783 (2005) arXiv: hep-th/0505016.
23. Oriti, D.: Quantum Gravity. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds.) Birkhauser, Basel (2007). arXiv: gr-qc/0512103.
24. De Pietri R., Petronio C.: Feynman diagrams of generalized matrix models and the associated manifolds in dimension 4. J. Math. Phys. 41, 6671-6688 (2000) arXiv: gr-qc/0004045.
25. Barrett, J., Nash-Guzman, I.: arXiv: 0803. 3319 (gr-qc).
26. Engle J., Pereira R., Rovelli C.: The loop-quantum-gravity vertex-amplitude. Phys. Rev. Lett. 99, 161301 (2007) arXiv: 0705. 2388.
27. Engle J., Pereira R., Rovelli C.: Flipped spinfoam vertex and loop gravity. Nucl. Phys. B 798, 251 (2008) arXiv: 0708. 1236 [gr-qc].
28. Livine E. R., Speziale S.: A new spinfoam vertex for quantum gravity. Phys. Rev. D 76, 084028 (2007) arXiv: 0705. 0674 [gr-qc].
29. Freidel L., Krasnov K.: A new spin foam model for 4d gravity. Class. Quant. Grav. 25, 125018 (2008) arXiv: 0708. 1595 [gr-qc].
30. Conrady F., Freidel L.: On the semiclassical limit of 4d spin foam models. Phys. Rev. D 78, 104023 (2008) arXiv: 0809. 2280 [gr-qc].
31. Bonzom V., Livine E. R., Smerlak M., Speziale S.: Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model. Nucl. Phys. B 804, 507 (2008) arXiv: 0802. 3983 [gr-qc].
32. Freidel L., Gurau R., Oriti D.: Group field theory renormalization-the 3d case: power counting of divergences. Phys. Rev. D 80, 044007 (2009) arXiv: 0905. 3772 [hep-th].
33. Magnen, J., Noui, K., Rivasseau, V., Smerlak, M.: arXiv: 0906. 5477 [hep-th].
34. Adbesselam, A.: On the volume conjecture for classical spin networks. arXiv: 0904. 1734[math. GT].
35. Geloun, J. B., Magnen, J., Rivasseau, V.: Bosonic Colored Group Field Theory. arXiv: 0911. 1719 [hep-th].
36. Kirchhoff G.: Uber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Ströme gefürht wird. Ann. Phys. Chem. 72, 497-508 (1847).
37. Tutte W. T.: Graph Theory. Addison-Wesley, Reading (1984).
38. 't Hooft G., Veltman M.: Regularization and renormalization of gauge fields. Nucl. Phys. B44(1), 189-213 (1972).
39. Crapo H. H.: The Tutte polynomial. Aequationes Mathematicae 3, 211-229 (1969).
40. Sokal, A.: The multivariate Tutte polynomial (alias Potts model) for graphs and matroids, Surveys in combinatorics 2005, pp. 173-226. London Math. Soc. Lecture Note Ser., vol. 327. Cambridge University Press, Cambridge (2005). arXiv: math/0503607.
41. Jackson, B., Procacci, A., Sokal, A. D.: Complex zero-free regions at large {pipe}q{pipe} for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights. arXiv: 0810. 4703v1 [math. CO].
42. Bollobás B., Riordan O.: A polynomial invariant of graphs on orientable surfaces. Proc. Lond. Math. Soc. 83, 513-531 (2001).
43. Bollobás B., Riordan O.: A polynomial of graphs on surfaces. Math. Ann. 323, 81-96 (2002).
44. Ellis-Monaghan, J., Merino, C.: Graph polynomials and their applications. I. The Tutte polynomial. arXiv: 0803. 3079.
45. Ellis-Monaghan, J., Merino, C.: Graph polynomials and their applications. II. Interrelations and interpretations. arXiv: 0806. 4699.
46. Gurau R., Rivasseau V.: Parametric representation of noncommutative field theory. Commun. Math. Phys. 272, 811 (2007) arXiv: math-ph/0606030.
47. Rivasseau V., Tanasa A.: Parametric representation of 'critical' noncommutative QFT models. Commun. Math. Phys. 279, 355 (2008) arXiv: math-ph/0701034.
48. Tanasa, A.: Parametric representation of a translation-invariant renormalizable noncommutative model. arXiv: 0807. 2779 [math-ph].
49. Krajewski, T., Rivasseau, V., Tanasa, A., Wang, Z.: Topological Graph Polynomials and Quantum Field Theory. Part I. Heat Kernel Theories. arXiv: 0811. 0186 [math-ph].
50. Bollobás B., Riordan O.: A Tutte polynomial for coloured graphs. Combin. Probab. Comput. 8, 45-93 (1999).