Towards gauge theory for a class of commutative and non-associative fuzzy spaces

Journal of High Energy Physics

Volumn 8, Issue 3, 2004, Pages 779-808

  Ramgoolam, Sanjaye ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

D branes; Gauge Symmetry; M(atrix) Theories; Space Time Symmetries

Indexed keywords

EID: 23044450262     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2004/03/034     Document Type: Article

References (37)

1. H. Grosse, C. Klimčík and P. Prešnajder, Finite quantum field theory in noncommutative geometry, Commun. Math. Phys.180 (1996) 429 [hep-th/9602115].
2. J. Castelino, S.M. Lee and I.W. Taylor, Longitudinal 5-branes as 4-spheres in matrix theory, Nucl. Phys. B526 (1998) 334 [hep-th/9712105].
3. N.R. Constable, R.C. Myers and O. Tafjord, Non-abelian brane intersections, J. High Energy Phys.06 (2001) 023 [hep-th/0102080].
4. J. Madore, The fuzzy sphere, Class. and Quant.Grav.9 (1992) 69.
5. S. Ramgoolam, On spherical harmonics for fuzzy spheres in diverse dimensions, Nucl. Phys. B610 (2001) 461 [hep-th/0105006].
6. P.M. Ho and S. Ramgoolam, Higher dimensional geometries from matrix brane constructions, Nucl. Phys. B627 (2002) 266 [hep-th/0111278].
7. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M-theory as a matrix model: a conjecture, Phys. Rev. D55 (1997) 5112 [hep-th/9610043].
8. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B498 (1997) 467 [hep-th/9612115].
9. O.J. Ganor, S. Ramgoolam and I.W. Taylor, Branes, fluxes and duality in M(atrix)-theory, Nucl. Phys. B492 (1997) 191 [hep-th/9611202].
10. A. Connes, M.R. Douglas and A. Schwarz, Noncommutative geometry and matrix theory: compactification on tori, J. High Energy Phys.02 (1998) 003 [hep-th/9711162].
11. H. Aoki et al., Noncommutative Yang-Mills in IIB matrix model, Nucl. Phys. B565 (2000) 176 [hep-th/9908141].
12. N. Seiberg, A note on background independence in noncommutative gauge theories, matrix model and tachyon condensation, J. High Energy Phys.09 (2000) 003 [hep-th/0008013].
13. D.A. Lowe, H. Nastase and S. Ramgoolam, Massive IIA string theory and matrix theory compactification, Nucl. Phys. B667 (2003) 55 [hep-th/0303173].
14. S. Iso, Y. Kimura, K. Tanaka and K. Wakatsuki, Noncommutative gauge theory on fuzzy sphere from matrix model, Nucl. Phys. B604 (2001) 121 [hep-th/0101102].
15. 3 and the fuzzy sphere, Phys. Rev. D 66 (2002) 025025 [hep-th/0110291].
16. E. Batista and S. Majid, Noncommutative geometry of angular momentum space U(su(2)), J. Math. Phys.44 (2003) 107 [hep-th/0205128].
17. T.L. Curtright, G.I. Ghandour and C.K. Zachos, Quantum algebra deforming maps, Clebsch-Gordan coefficients, coproducts, U and R matrices, J. Math. Phys.32 (1991) 676.
18. V.G. Drinfeld, Quasi-Hopf algebras, Leningrad Math. J.1 (1990) 1419.
19. 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].
20. A. Jevicki, M. Mihailescu and S. Ramgoolam, Hidden classical symmetry in quantum spaces at roots of unity: from q-sphere to fuzzy sphere, hep-th/0008186.
21. H. Grosse, J. Madore and H. Steinacker, Field theory on the q-deformed fuzzy sphere, II. Quantization, J. Geom. Phys.43 (2002) 205 [hep-th/0103164].
22. S. Majid, Foundations of quantum group theory CUP 1995.
23. V. Chari and A. Pressley, A guide to quantum groups, CUP 1994.
24. I.S. Gradshtein and I.M. Rhyzik, Tables of integrals, series and products, Academic Press 2000, eq. 0.160.2.
25. N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys.09 (1999) 032 [hep-th/9908142].
26. I.S. Gradshtein and I.M. Rhyzik, Tables of integrals, series and products, Academic Press 2000, eq. 0.156.1
27. P. Cook, R. de Mello Koch and J. Murugan, Nonabelian bionic brane intersections, Phys. Rev. D68 (2003) 126007 [hep-th/0306250].
28. Y. Kimura, Noncommutative gauge theory on fuzzy four-sphere and matrix model, Nucl. Phys. B637 (2002) 177 [hep-th/0204256].
29. S.C. Zhang, J.P. Hu, A four dimensional generalization of the quantum Hall effect, Science294 (2001) 823.
30. B.A. Bernevig, C.H. Chern, J.P. Hu, N. Toumbas and S.C. Zhang, Effective field theory description of the higher dimensional quantum Hall liquid, Ann. Phys. (NY)300 (2002) 185 [cond-mat/0206164].
31. A. Jevicki and S. Ramgoolam, Non-commutative gravity from the AdS/CFT correspondence, J. High Energy Phys.04 (1999) 032 [hep-th/9902059].
32. M. Berkooz and H. Verlinde, Matrix theory, AdS/CFT and Higgs-Coulomb equivalence, J. High Energy Phys.II (1999) 037 [hep-th/9907100].
33. R. Brandenberger and P.-M. Ho, Noncommutative spacetime, stringy spacetime uncertainty principle and density fluctuations, Phys. Rev. D66 (2002) 023517 [hep-th/0203119].
34. C.M. Hull, Lectures on W gravity, W geometry and W strings, hep-th/9302110.
35. P.M. Ho, Making non-associative algebra associative, J. High Energy Phys.11 (2001) 026 [hep-th/0103024].
36. L. Cornalba and R. Schiappa, Nonassociative star product deformations for D-brane worldvolumes in curved backgrounds, Commun. Math. Phys.225 (2002) 33 [hep-th/0101219].
37. I.A. Batalin and G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D28 (1983) 2567.