A matrix phase for the Φ4 scalar field on the fuzzy sphere

Journal of High Energy Physics

Volumn 8, Issue 4, 2004, Pages 1801-1820

  Martin, Xavier ^a  

^a DUBLIN INSTITUTE FOR ADVANCED STUDIES   (Ireland)

Author keywords

Non Commutative Geometry; Nonperturbative Effects

Indexed keywords

EID: 23044463835     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. H. Grosse and P. Prešnajder, The Dirac operator on the fuzzy sphere, Lett. Math. Phys. 33 (1995) 171;
2. H. Grosse, C. Klimčík and P. Prešnajder, Topologically nontrivial field configurations in noncommutative geometry, Commun. Math. Phys. 178 (1996) 507 [hep-th/9510083];
3. Field theory on a supersymmetric lattice, Commun. Math. Phys. 185 (1997) 155 [hep-th/9507074];
4. H. Grosse and P. Prešnajder, A noncommutative regularization of the Schwinger model, Lett. Math. Phys. 46 (1998) 61;
5. H. Grosse, C. Klimčík and P. Prešnajder, Finite quantum field theory in noncommutative geometry, Commun. Math. Phys. 180 (1996) 429 [hep-th/9602115];
6. N = 2 superalgebra and non-commutative geometry, hep-th/9603071.
7. S. Baez, A.P. Balachandran, S. Vaidya and B. Ydri, Monopoles and solitons in fuzzy physics, Commun. Math. Phys. 208 (2000) 787 [hep-th/9811169];
8. P. Balachandran, T.R. Govindarajan and B. Ydri, The fermion doubling problem and noncommutative geometry, Mod. Phys. Lett. A 15 (2000) 1279 [hep-th/9911087];
9. 2, J. Geom. Phys. 42 (2002) 28 [hep-th/0103023];
10. B. Ydri, Fuzzy physics, hep-th/0110006.
11. A. Connes, Noncommutative Geometry, Academic Press, San Diego 1994.
12. A.P. Balachandran, B.P. Dolan, J.-H. Lee, X. Martin and D. O'Connor, Fuzzy complex projective spaces and their star-products, J. Geom. Phys. 43 (2002) 184 [hep-th/0107099];
13. G. Alexanian, A. Pinzul and A. Stern, Generalized coherent state approach to star products and applications to the fuzzy sphere, Nucl. Phys. B 600 (2001) 531 [hep-th/0010187].
14. S. Vaidya and B. Ydri, On the origin of the UV-IR mixing in noncommutative matrix geometry, Nucl. Phys. B 671 (2003) 401 [hep-th/0305201];
15. New scaling limit for fuzzy spheres, hep-th/0209131.
16. B.P. Dolan and D. O'Connor, A fuzzy three sphere and fuzzy tori, J. High Energy Phys. 10 (2003) 060 [hep-th/0306231].
17. 4, J. High Energy Phys. 11 (2003) 051 [hep-th/0212170].
18. J. Ambjørn and S. Catterall, Stripes from (noncommutative) stars, Phys. Lett. B 549 (2002) 253 [hep-lat/0209106];
19. 4 model, Acta Phys. Polon. B34 (2003) 4711 [hep-th/0309216];
20. The renormalizability of 2d Yang-Mills theory on a non-commutative geometry, J. High Energy Phys. 09 (2002) 009 [hep-th/0203151].
21. T. Azuma, S. Bai, K. Nagao and J. Nishimura, Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term, hep-th/0401038.
22. J. Madore, The fuzzy sphere, Class. and Quant. Grav. 9 (1992) 69.
23. D. O'Connor, Field theory on low dimensional fuzzy spaces, Mod. Phys. Lett. A 18 (2003) 2423.
24. P. Prešnajder, The origin of chiral anomaly and the noncommutative geometry, J. Math. Phys. 41 (2000) 2789 [hep-th/9912050];
25. A.P. Balachandran, B.P. Dolan, J. Lee, X. Martin and D. O'Connor, Fuzzy complex projective spaces and their star products, J. Geom. Phys. 43 (2002) 184 [hep-th/0107099].
26. C.-S. Chu, J. Madore and H. Steinacker, Scaling limits of the fuzzy sphere at one loop, J. High Energy Phys. 08 (2001) 038 [hep-th/0106205];
27. 4 models on the fuzzy sphere and their continuum limits, J. High Energy Phys. 03 (2002) 013 [hep-th/0109084].
28. I. Montvay and C. Munster, Quantum field theory on a lattice, Cambridge University Press, Cambridge 1997.
29. F. Garcia, X. Martin, and D. O'Connor, in preparation.
30. S. Vaidya, Scalar multi-solitons on the fuzzy sphere, J. High Energy Phys. 01 (2002) 011 [hep-th/0109102].