Deformations of closed strings and topological open membranes

Journal of High Energy Physics

Volumn 5, Issue 6, 2001, Pages

  Hofman, Christiaan ^a   Ma, Whee Ky ^a,b  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Chern simons theories; Conformai field models in string theory; Differential and algebraic geometry; Topological field theories

Indexed keywords

EID: 33744547661     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2001/06/033     Document Type: Article

References (43)

1. 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].
2. M.R. Douglas and C. Hull, D-branes and the noncommutative torus, J. High Energy Phys. 02 (1998) 008 [hep-th/9711165].
3. C. Hofman and E. Verlinde, U-duality of Born-Infeld on the noncommutative two-torus, J. High Energy Phys. 12 (1998) 010 [hep-th/9810116].
4. V. Schomerus, D-branes and deformation quantization, J. High Energy Phys. 06 (1999) 030 [hep-th/9903205].
5. N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09 (1999) 032 [hep-th/9908142].
6. M. Kontsevich, Deformation quantisation of Poisson manifolds, I, math.QA/9709180.
7. M. Kontsevich, Operads and motives in deformation quantisation, math.QA/9904055.
8. D. Tamarkin, Another proof of M. Kontsevich formality theorem, math.QA/9803025.
9. M. Kontsevich, Y. Soibelman, Deformations of Algebras over Operads and Deligne’s Conjecture math.QA/0001151.
10. A.S. Cattaneo and G. Felder, A path integral approach to the Kontsevich quantisation formula, math.QA/9902090.
11. C. Hofman and W.-K. Ma, Deformations of topological open strings, J. High Energy Phys. 01 (2001) 035 [hep-th/0006120].
12. C.I. Lazaroiu, On the structure of open-closed topological field theory in two dimensions, Nucl. Phys. B 603 (2001) 497 [hep-th/0010269].
13. E. Witten and B. Zwiebach, Algebraic structures and differential geometry in 2 − d string theory, Nucl. Phys. B 377 (1992) 55 [hep-th/9201056].
14. B. Zwiebach, Closed string field theory: quantum action and the b-v master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084].
15. J. Stasheff, Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli spaces, hep-th/9304061.
16. T. Kimura, A.A. Voronov, G.J. Zuckerman, Homotopy Gerstenhaber algebras and topological field theory, q-alg/9602009.
17. D. Tamarkin, The deformation complex of a d-algebra is a (d + 1)-algebra, math.QA/0010072.
18. E. Bergshoeff, D.S. Berman, J.P. van der Schaar and P. Sundell, A noncommutative M-theory five-brane, Nucl. Phys. B 590 (2000) 173 [hep-th/0005026].
19. S. Kawamoto and N. Sasakura, Open membranes in a constant C-field background and noncommutative boundary strings, J. High Energy Phys. 07 (2000) 014 [hep-th/0005123].
20. Y. Matsuo and Y. Shibusa, Volume preserving diffeomorphism and noncommutative branes, J. High Energy Phys. 02 (2001) 006 [hep-th/0010040].
21. A. Losev, G. Moore and S.L. Shatashvili, M & m’s, Nucl. Phys. B 522 (1998) 105 [hep-th/9707250].
22. O. Aharony, A brief review of ’little string theories’, Class. and Quant. Grav. 17 (2000) 929 [hep-th/9911147].
23. R. Gopakumar, S. Minwalla, N. Seiberg and A. Strominger, Om theory in diverse dimensions, J. High Energy Phys. 08 (2000) 008 [hep-th/0006062].
24. E. Bergshoeff, D.S. Berman, J.P. van der Schaar and P. Sundell, Critical fields on the m5-brane and noncommutative open strings, Phys. Lett. B 492 (2000) 193 [hep-th/0006112].
25. E. Witten, Two-dimensional gravity and intersection theory on moduli space, Surv. Diff. Geom. 1 (1991) 243-31.
26. R. Dijkgraaf, E. Verlinde and H. Verlinde, Topological Open Strings in d < 1, Nucl. Phys. B 352 (1991) 59.
27. J.-S. Park, Topological open p-branes, hep-th/0012141.
28. J. Stasheff, Homotopy associativity of H-spaces, I and II, Trans. Amer. Math. Soc. 108 (1963) 275 and 293.
29. ∞-algebras and the cyclic bar complex, Ill. J. Math. 34, No. 2 (1990) 256.
30. E. Getzler and J.D. S. Jones, Operads, homotopy algebra and iterated integrals for double loop spaces, hep-th/9403055.
31. B. Zwiebach, Oriented open-closed string theory revisited, Annals Phys. 267 (1998) 193 [hep-th/9705241].
32. M. Kontsevich, Feynman diagrams and low-dimensional topology, First European Congress of Mathematics, 1990-1992 Birkhäuser (1993) 173.
33. T. Kimura, J. Stasheff and A.A. Voronov, On operad structures of moduli spaces and string theory, Comm. Math. Phys. 171 (1995) 1 [hep-th/9307114].
34. B.H. Lian and G.J. Zuckerman, Algebraic and geometric structures in string backgrounds, hep-th/9506210.
35. D. Tamarkin and B. L. Tsygan, Noncommutative differential calculus, homotopy BV algebras and formality conjectures, math.KT/0002116.
36. E. Verlinde, The master equation of 2-d string theory, Nucl. Phys. B 381 (1992) 141 [hep-th/9202021].
37. C. Hofman, J.-S. Park, and S.-M. Lee, to be published.
38. E. Witten, Chern-Simons gauge theory as a string theory, hep-th/9207094.
39. T. Courant, Dirac manifolds, Trans. Amer. Math. Soc. 319 (1990) 631.
40. D. Roytenberg, Courant algebroids, derived brackets and even symplectic supermani-folds, Ph.D. thesis, University of California at Berekeley (1999), math.DG/9910078.
41. Z.-J. Liu, A. Weinstein, and P. Xu, Manin triplesa for Lie bialgebroids, J. Diff. Geom. 45 (1997) 547 [dg-ga/9508013].
42. C. Hofman and J.-S. Park, work in progress.
43. R. Bott and L.W. Tu, Differential forms in algebraic Topology, Springer-Verlag, New York 1982.