The dual of pure non-Abelian lattice gauge theory as a spin foam model

Nuclear Physics B

Volumn 598, Issue 1-2, 2001, Pages 400-426

  Oeckl, Robert ^a   Pfeiffer, Hendryk ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

11.15.Ha; 11.15.Me; 12.38.Aw; Duality; Lattice gauge theory; Non Abelian; Spin foam; Spin network; Wilson loop

Indexed keywords

EID: 0035911865     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(00)00770-7     Document Type: Article

References (28)

1. Kramers H.A., Wannier G.H. Statistics of the two-dimensional ferromagnet. Part I. Phys. Rev. 60:1941;252-262.
2. Savit R. Duality in field theory and statistical systems. Rev. Mod. Phys. 52:(2):1980;453-487.
3. Reisenberger M.P. World sheet formulation of gauge theories and gravity. gr-qc/9412035.
4. Iwasaki J. A definition of the Ponzano-Regge quantum gravity model in terms of surfaces. J. Math. Phys. 36:1995;6288-6298.
5. Reisenberger M.P., Rovelli C. `Sum over surfaces' form of loop quantum gravity. Phys. Rev. D. 56:1997;3490-3508.
6. Baez J.C. Spin foam models. Class. Quant. Grav. 15:(7):1998;1827-1858 gr-qc/9709052.
7. Baez J.C. An introduction to spin foam models of quantum gravity and BF theory. Geometry and Quantum Physics. Lecture Notes in Physics. 543:2000;Springer, Berlin, gr-qc/9905087.
8. Wilson K.G. Confinement of quarks. Phys. Rev. D. 10:(8):1974;2445-2459.
9. Banks T., Myerson R., Kogut J.B. Phase transitions in Abelian lattice gauge theories. Nucl. Phys. B. 129:1977;493-510.
10. Peskin M.E. Mandelstam-'t Hooft duality in Abelian lattice models. Ann. Phys. 113:1978;122-152.
11. Fröhlich J., Marchetti P.-A. Magnetic monopoles and charged states in four-dimensional Abelian lattice gauge theory. Europhys. Lett. 2:(12):1986;933-940.
12. Fröhlich J., Marchetti P.-A. Soliton quantization in lattice field theories. Commun. Math. Phys. 112:1987;343-383.
13. Guth A. Existence proof of a nonconfining phase in four-dimensional U(1) lattice gauge theory. Phys. Rev. D. 21:1980;2291-2307.
14. Fröhlich J., Spencer T. Massles phases and symmetry restoration in Abelian gauge theories and spin systems. Commun. Math. Phys. 83:1982;411-454.
15. Göpfert M., Mack G. Proof of confinement of static quarks in 3-dimensional U(1) lattice gauge theory for all values of the coupling constant. Commun. Math. Phys. 82:1982;545-606.
16. Polley L., Wiese U.-J. Monopole condensate and monopole mass in U(1) lattice gauge theory. Nucl. Phys. B. 356:1991;629-654.
17. Jersák J., Neuhaus T., Pfeiffer H. Scaling analysis of the magnetic monopole mass and condensate in the pure U(1) lattice gauge theory. Phys. Rev. D. 60:(5):1999;054502 hep-lat/9903034.
18. Jaimungal S. Wilson loops, Bianchi constraints and duality in Abelian lattice models. Nucl. Phys. B. 542:1999;441-470 hep-th/9808018.
19. Anishetty R., Cheluvaraja S., Sharatchandra H.S., Mathur M. Dual of 3 -dimensional pure SU(2) lattice gauge theory and the Ponzano-Regge model. Phys. Lett. B. 314:1993;387-390.
20. Diakonov D., Petrov V. Yang-Mills theory in three dimensions as quantum gravity theory. hep-th/9912268.
21. H. Grosse, K.-G. Schlesinger, Duals for non-Abelian lattice gauge theories by categorial methods, Erwin Schrödinger Institute preprint ESI 561, Vienna, 1998.
22. Batrouni G.G. Plaquette formulation and the Bianchi identity for lattice gauge theories. Nucl. Phys. B. 208:1982;467-483.
23. Hong-Mo Ch., Faridani J., Tsun T.S. Generalized dual symmetry for non-Abelian Yang-Mills fields. Phys. Rev. D. 53:(12):1996;7293-7305.
24. Bröcker T., Dieck T. Representations of Compact Lie Groups. Graduate Texts in Mathematics. 98:1985;Springer, New York.
25. Carter R., Segal G., Macdonald I. Lectures on Lie Groups and Lie Algebras. London Mathematical Society Student Texts. 32:1995;Cambridge Univ. Press, Cambridge.
26. Rothe H.J. Lattice Gauge Theories - An Introduction. 1992;World Scientific, Singapore.
27. Montvay I., Münster G. Quantum Fields on a Lattice. 1994;Cambridge Univ. Press, Cambridge.
28. Drouffe J.-M., Zuber J.-B. Strong coupling and mean-field methods in lattice gauge theories. Phys. Rep. 102:(1,2):1983;1-119.