Spin Models, TQFTs and Their Hierarchical Structure

  • G. Carbone
  • M. Carfora
  • A. Marzuoli
Conference paper


State sum models based on the recoupling theory of SU(2) angular momenta can be defined in any dimension d, and the corresponding hierarchy includes the Ponzano-Regge model in d = 3 and the Crane-Yetter invariant in d = 4. Here we establish an equivalence between each of these spin models and a corresponding B F theory by exploiting suitable d-dimensional generalizations of the Ooguri’s approach in d = 3.


Partition Function Flat Connection Auxiliary Surface Topological Quantum Field Theory Contractible Loop 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Birmingham, D., Blau, I., Rakowski, M., Thomson, G. (1991): Phys. Rep. 209, 129MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Carbone, G., Carfora, M., Marzuoli, A. (2001): Nucl. Phys. B 595 [PM], 654MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Ponzano, G., Regge, T. (1968): Semiclassical limit of Racah coefficients, in Spectroscopic and Group Theoretical Methods in Physics, ed. by F. Bloch, S.G. Cohen, A. De Shalit, S. Sambursky, I. Talmi, North-Holland Publ. Co., Amsterdam, p. 1Google Scholar
  4. 4.
    Crane, L., Kauffman, L.H., Yetter, D.N.: State sum invariants of four manifolds; hep-th/9409167Google Scholar
  5. 5.
    Ooguri, H. (1992): Nucl. Phys. B 382, 276MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Broda, B. (1995): A gauge-field approach to 3-and 4-manifold invariants, in Symplectic singularities and geometry of gauge field, ed. by R. Budzynski, S. Janeczk, O.W. Kondracki, A.F. Kunzle, Polish Academy of Science, Warsaw, p. 201Google Scholar
  7. 7.
    Roberts, J. (1995): Topology 34, 771MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Carbone, G. (2000): Ph.D Thesis, S.LS.S.A.-I.S.A.S., TriesteGoogle Scholar
  9. 9.
    Oriti, D., Williams, R.M. (2001): Phys. Rev. D 63, 024022MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Freidel, L., Krasnov, K. (1999): Adv. Theor. Math. Phys. 2, 1183MathSciNetGoogle Scholar
  11. 11.
    Yutsis, A.P., Levinson, LB., Vanagas, V.V. (1962): The Mathematical Apparatus of the Theory of Angular Momentum. Published for the National Science Foundation by the Israel Program for Scientific Translation, JerusalemMATHGoogle Scholar

Copyright information

© Springer-Verlag Italia 2002

Authors and Affiliations

  1. 1.S.I.S.S.A.TriesteItaly
  2. 2.Ecole Normale Supérieure de Lyon, Laboratoire de PhysiqueLyon, Cedex 07France
  3. 3.Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, and Istituto Nazionale di Fisica Nucleare, Sezione di PaviaPaviaItaly

Personalised recommendations