A fuzzy three sphere and fuzzy tori

Journal of High Energy Physics

Volumn 7, Issue 10, 2003, Pages 1501-1516

  Dolan, Brian P ^a,b   O'Connor, Denjoe ^b  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b DUBLIN INSTITUTE FOR ADVANCED STUDIES   (Ireland)

Author keywords

Non Commutative Geometry; Renormalization Regularization and Renormalons

Indexed keywords

EID: 23044464745     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/10/060     Document Type: Article

References (36)

1. I. Montvay and G. Munster, Quantum field on a lattice, Cambridge University Press, Cambridge 1997.
2. 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].
3. G. Alexanian, A.P. Balachandran, G. Immirzi and B. Ydri, Fuzzy CP(2), J. Geom. Phys. 42 (2002) 28 [hep-th/0103023].
4. 4, hep-th/0212170.
5. A.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];
6. The fermion doubling problem and noncommutative geometry, II, hep-th/0006216;
7. A.P. Balachandran and G. Immirzi, The fuzzy Ginsparg-Wilson algebra: a solution of the fermion doubling problem, Phys. Rev. D 68 (2003) 065023 [hep-th/0301242].
8. A.P. Balachandran, S. Kurkcuoglu and E. Rojas, The star product on the fuzzy supersphere, J. High Energy Phys. 07 (2002) 056 [hep-th/0204170];
9. H. Grosse, C. Klimčik and P. Prešnajder, N = 2 superslgebra and non-commutative goemetry, hep-th/9603071;
10. Field theory on a supersymmetric lattice, Commun. Math. Phys. 185 (1997) 155 [hep-th/9507074];
11. H. Grosse and G. Reiter, The fuzzy supersphere, J. Geom. Phys. 28 (1998) 349 [math-ph/9804013].
12. A.Y. Alekseev, A. Recknagel and V. Schomerus, Non-commutative world-volume geometries: branes on SU(2) and fuzzy spheres, J. High Energy Phys. 09 (1999) 023 [hep-th/9908040].
13. Y. Hikida, M. Nozaki and Y. Sugawara, Formation of spherical d2-brane from multiple D0-branes, Nucl. Phys. B 617 (2001) 117 [hep-th/0101211].
14. H. Grosse, C. Klimčík and P. Prešnajder, Towards finite quantum field theory innoncommutative geometry, Int. J. Theor. Phys. 35 (1996) 231-244 [hep-th/9505175];
15. H. Grosse and A. Strohmaier, Noncommutative geometry and the regularization problem of 4d quantum field theory, Lett. Math. Phys. 48 (1999) 163 [hep-th/9902138].
16. H. Grosse, C. Klimčík and P. Prešnajder, Topologically nontrivial field configurations in noncommutative geometry, Commun. Math. Phys. 178 (1996) 507 [hep-th/9510083];
17. H. Grosse and P. Prešnajder, A noncommutative regularization of the schwinger model, Lett. Math. Phys. 46 (1998) 61.
18. P. Prešnajder, The origin of chiral anomaly and the noncommutative geometry, J. Math. Phys. 41 (2000) 2789 [hep-th/9912050].
19. A.P. Balachandran and S. Vaidya, Instantons and chiral anomaly in fuzzy physics, Int. J. Mod. Phys. A 16 (2001) 17 [hep-th/9910129];
20. S. Baez, A.P. Balachandran, B. Idri and S. Vaidya, Monopoles and solitons in fuzzy physics, Commun. Math. Phys. 208 (2000) 787 [hep-th/9811169].
21. J. Madore, The fuzzy sphere, Class, and Quant. Grav. 9 (1992) 69.
22. S. Ramgoolam, On spherical harmonics for fuzzy spheres in diverse dimensions, Nucl. Phys. B 610 (2001) 461 [hep-th/0105006].
23. Y. Kimura, On higher dimensional fuzzy spherical branes, Nucl. Phys. B 664 (2003) 512 [hep-th/0301055].
24. S. Ramgoolam, Higher dimensional geometries related to fuzzy odd- dimensional spheres, J. High Energy Phys. 10 (2002) 064 [hep-th/0207111].
25. P.-M. Ho and S. Ramgoolam, Higher dimensional geometries from matrix brane constructions, Nucl. Phys. B 627 (2002) 266 [hep-th/0111278].
26. A.P. Balachandran, B.P. Dolan, J.-H. Lee, X. Martin and D. O'Connor, Fuzzy complex protective spaces and their star-products, J. Geom. Phys. 43 (2002) 184 [hep-th/0107099].
27. J. Fröhlich and K. Gawȩdzki, Conformal field theory and geometry of strings, lectures given at Mathematical Quantum Theory Conference, Vancouver, Canada, 4-8 Aug 1993,
28. published in Vancouver 1993, proceedings, Mathematical quantum theory, Vol. 1 57-97, [hep-th/9310187].
29. B.P. Dolan, Denjoe O'Connor and P. Prešnajder, in preparation.
30. A. Connes, Noncommutative geometry, Academic Press, London 1994.
31. F.A. Berezin, General concept of quantization, Commun. Math. Phys. 40 (1975) 153.
32. 4 models on the fuzzy sphere and their continuum limits, J. High Energy Phys. 03 (2002) 013 [hep-th/0109084].
33. D.A. Varshalovich, A.N. Moskalev and V.K. Khersonskii, Quantum theory of angular momentum, World Scientific, Singapore 1988.
34. 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].
35. W. Fulton and J. Harris, Representation theory: a first course, Graduate Texts in Mathematics 129, Springer, 1991
36. B.P. Dolan and C. Nash, Chiral fermions and Spin(C) structures on matrix approximations to manifolds, J. High Energy Phys. 07 (2002) 057 [hep-th/0207007].