Abstract
When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side. Considering a general class of T3-fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (eiJ and Ω) in dual geometries under fiberwise T–duality, and study the transformations of the NS flux and the components of intrinsic torsion. A complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with NS flux.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Gurrieri, S., Louis, J., Micu, A., Waldram, D.: Mirror symmetry in generalized Calabi-Yau compactifications. Nucl. Phys. B 654, 61 (2003)
Vafa, C.: Superstrings and topological strings at large N. J. Math. Phys. 42, 2798 (2001)
Strominger, A., Yau, S.T., Zaslow, E.: Mirror symmetry is T-duality. Nucl. Phys. B 479, 243 (1996)
Hitchin, N.: Generalized Calabi-Yau manifolds. http://arxiv.org/abs/0209099, 2002
Leung, N.C., Yau, S.T., Zaslow, E.: From special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform. Adv. Theor. Math. Phys. 4, 1319 (2002)
Marino, M., Minasian, R., Moore, G.W., Strominger, A.: Nonlinear instantons from supersymmetric p-branes. JHEP 0001, 005 (2000)
Douglas, M.R., Fiol, B., Romelsberger, C.: Stability and BPS branes. http://arxiv.org/abs/hepth/0002037, 2000
Strominger, A.: Superstrings With Torsion. Nucl. Phys. B 274, 253 (1986)
Gauntlett, J.P., Martelli, D., Pakis, S., Waldram, D.: G-structures and wrapped NS5-branes. Commun. Math. Phys. 247, 421–445 (2004)
Cardoso, G.L., Curio, G., Dall’Agata, G., Lust, D., Manousselis, P., Zoupanos, G.: Non-Kaehler string backgrounds and their five torsion classes. Nucl. Phys. B 652, 5 (2003)
Bouwknegt, P., Evslin, J., Mathai, V.:T-duality: Topology change from H-flux. Commun. Math. Phys. 249, 383–415 (2004)
Hassan, S.F.: SO(d,d) transformations of Ramond-Ramond fields and space-time spinors. Nucl. Phys. B 583, 431 (2000)
Joyce, D.D.: Compact manifolds with special holonomy. Oxford: Oxford Univ. Press, 2000
Kaste, P., Minasian, R., Tomasiello, A.: Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G-structures. JHEP 0307, 004 (2003)
Liu, J.T., Minasian, R.: U-branes and T**3 fibrations. Nucl. Phys. B 510, 538 (1998)
Hitchin, N.: Stable forms and special metrics. In: Global differential geometry: the mathematical legacy of Alfred Gray, Volume 288 of Contemp. Math. , Providence RI: AMS, 2001, pp. 70–89
Chiossi, S., Salamon, S.: The intrinsic torsion of SU(3) and G2 structures. In: Proc. conf. Differential Geometry, Valencia 2001, Singapore: World Scientific Publishing, 2002, pp. 115–133
Becker, K., Becker, M., Green, P.S., Dasgupta, K., Sharpe, E.: Compactifications of heterotic strings on non-Kaehler complex manifolds. II. Nucl. Phys. B 678, 19–100 (2004)
Rohm, R., Witten, E.: Annals Phys. 170, 454 (1986)
Grana, M., Polchinski, J.: Gauge / gravity duals with holomorphic dilaton. Phys. Rev. D 65 126005 (2002)
Kaste, P., Minasian, R., Petrini, M., Tomasiello, A.: Nontrivial RR two-form field strength and SU(3)-structure. Fortsch. Phys. 51, 764–768 (2003)
Kapustin, A.: Topological strings on noncommutative manifolds. Int. J. Geom. Math. Mod. Phys. 1, 49–81 (2004)
Kapustin, A., Orlov, D.: Vertex algebras, mirror symmetry, and D-branes: The case of complex tori. Commun. Math. Phys. 233, 79 (2003)
Author information
Authors and Affiliations
Additional information
Communicated by N.A. Nekrasov
Rights and permissions
About this article
Cite this article
Fidanza, S., Minasian, R. & Tomasiello, A. Mirror Symmetric SU(3)-Structure Manifolds with NS Fluxes. Commun. Math. Phys. 254, 401–423 (2005). https://doi.org/10.1007/s00220-004-1221-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-004-1221-5