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Defects, non-abelian t-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields

  • Eva Gevorgyan
  • Gor Sarkissian
Open Access
Article

Abstract

We construct topological defects generating non-abelian T-duality for isometry groups acting without isotropy. We find that these defects are given by line bundles on the correspondence space with curvature which can be considered as a non-abelian generalization of the curvature of the Poincarè bundle. We show that the defect equations of motion encode the non-abelian T-duality transformation. The Fourier-Mukai transform of the Ramond-Ramond fields generated by the gauge invariant flux of these defects is studied. We show that it provides elegant and compact way of computation of the transformation of the Ramond-Ramond fields under the non-abelian T-duality.

Keywords

D-branes Conformal Field Models in String Theory String Duality 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  2. [2]
    T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  3. [3]
    E. Bergshoeff, C.M. Hull and T. Ortín, Duality in the type-II superstring effective action, Nucl. Phys. B 451 (1995) 547 [hep-th/9504081] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    P. Meessen and T. Ortín, An SL(2, \( \mathbb{Z} \)) multiplet of nine-dimensional type-II supergravity theories, Nucl. Phys. B 541 (1999) 195 [hep-th/9806120] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    J. Polchinski, TASI lectures on D-branes, hep-th/9611050 [INSPIRE].
  6. [6]
    S.F. Hassan, T duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R. Benichou, G. Policastro and J. Troost, T-duality in Ramond-Ramond backgrounds, Phys. Lett. B 661 (2008) 192 [arXiv:0801.1785] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    K. Hori, D-branes, T duality and index theory, Adv. Theor. Math. Phys. 3 (1999) 281 [hep-th/9902102] [INSPIRE].zbMATHMathSciNetGoogle Scholar
  9. [9]
    P. Bouwknegt, J. Evslin and V. Mathai, T duality: topology change from H flux, Commun. Math. Phys. 249 (2004) 383 [hep-th/0306062] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  10. [10]
    K. Hori and Y. Oz, F theory, T duality on K3 surfaces and N = 2 supersymmetric gauge theories in four-dimensions, Nucl. Phys. B 501 (1997) 97 [hep-th/9702173] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    G. Sarkissian and C. Schweigert, Some remarks on defects and T-duality, Nucl. Phys. B 819 (2009) 478 [arXiv:0810.3159] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    K. Sfetsos and D.C. Thompson, On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys. B 846 (2011) 21 [arXiv:1012.1320] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, Ramond fields and coset geometries, JHEP 06 (2011) 106 [arXiv:1104.5196] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    G. Itsios, Y. Lozano, E. O’Colgain and K. Sfetsos, Non-abelian T-duality and consistent truncations in type-II supergravity, JHEP 08 (2012) 132 [arXiv:1205.2274] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  15. [15]
    G. Itsios, C. Núñez, K. Sfetsos and D.C. Thompson, Non-abelian T-duality and the AdS/CFT correspondence:new N = 1 backgrounds, Nucl. Phys. B 873 (2013) 1 [arXiv:1301.6755] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    J. Jeong, O. Kelekci and E. O Colgain, An alternative IIB embedding of F(4) gauged supergravity, JHEP 05 (2013) 079 [arXiv:1302.2105] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    X.C. de la Ossa and F. Quevedo, Duality symmetries from nonAbelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    A. Giveon and M. Roček, On non-abelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and G. Veneziano, Remarks on non-abelian duality, Nucl. Phys. B 435 (1995) 147 [hep-th/9409011] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  20. [20]
    E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, On non-abelian duality, Nucl. Phys. B 424 (1994) 155 [hep-th/9403155] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    Y. Lozano, NonAbelian duality and canonical transformations, Phys. Lett. B 355 (1995) 165 [hep-th/9503045] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  22. [22]
    Y. Lozano, Duality and canonical transformations, Mod. Phys. Lett. A 11 (1996) 2893 [hep-th/9610024] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  23. [23]
    J. Borlaf and Y. Lozano, Aspects of T duality in open strings, Nucl. Phys. B 480 (1996) 239 [hep-th/9607051] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    E.S. Fradkin and A.A. Tseytlin, Quantum equivalence of dual field theories, Annals Phys. 162 (1985) 31 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  25. [25]
    B.E. Fridling and A. Jevicki, Dual representations and ultraviolet divergences in nonlinear σ models, Phys. Lett. B 134 (1984) 70 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    C. Bachas, J. de Boer, R. Dijkgraaf and H. Ooguri, Permeable conformal walls and holography, JHEP 06 (2002) 027 [hep-th/0111210] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    V.B. Petkova and J.B. Zuber, Generalized twisted partition functions, Phys. Lett. B 504 (2001) 157 [hep-th/0011021] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    V. Petkova and J.-B. Zuber, Conformal field theories, graphs and quantum algebras, hep-th/0108236 [INSPIRE].
  29. [29]
    J. Fuchs, C. Schweigert and K. Waldorf, Bi-branes: target space geometry for world sheet topological defects, J. Geom. Phys. 58 (2008) 576 [hep-th/0703145] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  30. [30]
    I. Brunner, H. Jockers and D. Roggenkamp, Defects and D-brane monodromies, Adv. Theor. Math. Phys. 13 (2009) 1077 [arXiv:0806.4734] [INSPIRE].CrossRefzbMATHMathSciNetGoogle Scholar
  31. [31]
    G. Sarkissian, Defects in G/H coset, G/G topological field theory and discrete Fourier-Mukai transform, Nucl. Phys. B 846 (2011) 338 [arXiv:1006.5317] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    C. Bachas, I. Brunner and D. Roggenkamp, A worldsheet extension of O(d, d : Z), JHEP 10 (2012) 039 [arXiv:1205.4647] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    S. Elitzur, B. Karni, E. Rabinovici and G. Sarkissian, Defects, super-Poincaré line bundle and Fermionic T-duality, JHEP 04 (2013) 088 [arXiv:1301.6639] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    D. Huybrechts, Fourier-Mukai transforms in algebraic geometry, Oxford University Press, Oxford U.K. (2006).CrossRefzbMATHGoogle Scholar
  35. [35]
    C. Bartocci, U. Bruzzo and D.H. Ruipérez, Fourier-Mukai and Nahm transform and applications in mathematical physics, Progress in Mathematics volume 276, Birkhäuser, Spinger, Germany (2009).Google Scholar
  36. [36]
    R. Bott and L.W. Tu, Differential forms in algebraic topology, Springer, Germany (1995).Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsYerevan State UniversityYerevanArmenia
  2. 2.The Abdus Salam ICTPTriesteItaly

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