Index theorems on torsional geometries

Journal of High Energy Physics

Volumn 2007, Issue 8, 2007, Pages

  Kimura, Tetsuji ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Anomalies in field and string theories; Differential and algebraic geometry; Flux compactifications; Superstrings and heterotic strings

Indexed keywords

EID: 67650225501     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2007/08/048     Document Type: Article

References (50)

1. M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003].
2. M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102].
3. R. Blumenhagen, B. Körs, D. Lust and S. Stieberger, Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327].
4. S. Kachru, R. Kallosh, A. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240].
5. A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253.
6. P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46.
7. S. Salamon, Riemannian geometry and holonomy groups, Pitman Research Notes Math. 201, Longman (1989)
8. M. Falcitelli, A. Farinola and S. Salamon, Almost-Hermitian geometry, Diff. Geom. Appl. 4 (1994) 259
9. S. Salamon, Almost parallel structures, in Proceedings, Congress in memory of Alfred Gray, to appear in AMS Contemporary Mathematics, Contemp. Math. 288 (2001) 162 [math.DG/0107146]
10. 2 structures, math.DG/0202282.
11. J.P. Gauntlett, D. Martelli and D. Waldram, Superstrings with intrinsic torsion, Phys. Rev. D 69 (2004) 086002 [hep-th/0302158].
12. J.-M. Bismut, A local index theorem for non Kähler manifolds, Math. Ann. 284 (1989) 681.
13. S. Ivanov and G. Papadopoulos, Vanishing theorems and string backgrounds, Class, and Quant. Grav. 18 (2001) 1089 [math.DG/0010038].
14. G. Papadopoulos, KT and HKT geometries in strings and in black hole moduli spaces, hep-th/0201111.
15. K. Becker and L.-S. Tseng, Heterotic flux compactifications and their moduli, Nucl. Phys. B 741 (2006) 162 [hep-th/0509131].
16. M. Becker, L.-S. Tseng and S.-T. Yau, Moduli space of torsional manifolds, hep-th/0612290.
17. L. Alvarez-Gaumé, Supersymmetry and the Atiyah-Singer index theorem, Commun. Math. Phys. 90 (1983) 161;
18. A note on the Atiyah-Singer index theorem, J. Phys. A 16 (1983) 4177.
19. O. Alvarez, I.M. Singer and B. Zumino, Gravitational anomalies and the family's index theorem, Commun. Math. Phys. 96 (1984) 409.
20. K. Fujikawa, S. Ojima and S. Yajima, On the simple evaluation of chiral anomalies in the path integral approach, Phys. Rev. D 34 (1986) 3223.
21. T. Eguchi, P.B. Gilkey and A.J. Hanson, Gravitation, gauge theories and differential geometry, Phys. Rept. 66 (1980) 213.
22. M. Nakahara, Geometry, topology and physics, Institute of Physics Publishing, Bristol (1990).
23. M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, Cambridge University Press (1987).
24. N.E. Mavromatos, A note on the Atiyah-Singer index theorem for manifolds with totally antisymmetric H torsion, J. Phys. A 21 (1988) 2279.
25. S. Yajima, Gravitational anomalies with curl vanishing torsion, Hiroshima University Preprint HUPD-8901 (1989).
26. K. Peeters and A. Waldron, Spinors on manifolds with boundary: APS index theorems with torsion, JHEP 02 (1999) 024 [hep-th/9901016].
27. C.A. Scrucca and M. Serone, A note on the torsion dependence of D-brane RR couplings, Phys. Lett. B 504 (2001) 47 [hep-th/0010022].
28. T. Kimura and P. Yi, Comments on heterotic flux compactifications, JHEP 07 (2006) 030 [hep-th/0605247].
29. J. de Boer, B. Peeters, K. Skenderis and P. van Nieuwenhuizen, Loop calculations in quantum-mechanical non-linear sigma models sigma models with fermions and applications to anomalies, Nucl. Phys. B 459 (1996) 631 [hep-th/9509158].
30. F. Bastianelli and P. van Nieuwenhuizen, Path integrals and anomalies in curved space, Cambridge University Press (2006).
31. S. Ivanov and G. Papadopoulos, A no-go theorem for string warped compactifications, Phys. Lett. B 497 (2001) 309 [hep-th/0008232].
32. H.W. Braden, Supersymmetry with torsion, Phys. Lett. B 163 (1985) 171 [Erratum ibid. B167 (1986) 485]
33. Sigma models with torsion, Ann. Phys. (NY) 171 (1986) 433.
34. R. Rohm and E. Witten, The antisymmetric tensor field in superstring theory, Ann. Phys. (NY) 170 (1986) 454.
35. M. Gualtieri, Generalized complex geometry, math.DG/0401221.
36. A. Kapustin and Y. Li, Topological sigma-models with H-flux and twisted generalized complex manifolds, hep-th/0407249.
37. H.T. Nieh and M.L. Yan, An identity in Riemann-Carian geometry, J. Math. Phys. 23 (1982) 373.
38. O. Chandia and J. Zanelli, Topological invariants, instantons and chiral anomaly on spaces with torsion, Phys. Rev. D 55 (1997) 7580 [hep-th/9702025];
39. Supersymmetric particle in a spacetime with torsion and the index theorem, Phys. Rev. D 58 (1998) 045014 [hep-th/9803034].
40. L. Alvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269
41. L. Alvarez-Gaumé and P.H. Ginsparg, The structure of gauge and gravitational anomalies, Ann. Phys. (NY) 161 (1985) 423.
42. M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117.
43. C.M. Hull, Anomalies, ambiguities and superstrings, Phys. Lett. B 167 (1986) 51
44. Compactifications of the heterotic superstring, Phys. Lett. B 178 (1986) 357.
45. E.A. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B 328 (1989) 439.
46. G.L. Cardoso, G. Curio, G. Dall'Agata, D. Lust, P. Manousselis and G. Zoupanos, Non-Kähler string backgrounds and their five torsion classes, Nucl. Phys. B 652 (2003) 5 [hep-th/0211118].
47. K. Becker, M. Becker, K. Dasgupta and P.S. Green, Compactifications of heterotic theory on non-Kähler complex manifolds. I, JHEP 04 (2003) 007 [hep-th/0301161].
48. G. Lopes Cardoso, G. Curio, G. Dall'Agata and D. Lust, BPS action and super potential for heterotic string compactifications with fluxes, JHEP 10 (2003) 004 [hep-th/0306088].
49. J.-X. Fu and S.-T. Yau, The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampere equation, hep-th/0604063
50. K. Becker, M. Becker, J.-X. Fu, L.-S. Tseng and S.-T. Yau, Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory, Nucl. Phys. B 751 (2006) 108 [hep-th/0604137].