Skip to main content
SpringerLink
Log in

Self-duality of the D1-D5 near-horizon

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We explore fermionic T-duality and self-duality in the geometry AdS3 × S 3 × T 4 in type IIB supergravity. We explicitly construct the Killing spinors and the fermionic T- duality isometries and show that the geometry is self-dual under a combination of two bosonic AdS3 T-dualities, four fermionic T-dualities and either two additional T-dualities along T 4 or two T-dualities along S 3. In addition, we show that the presence of a B-field acts as an obstacle to self-duality, a property attributable to S-duality and fermionic T- duality not commuting. Finally, we argue that fermionic T-duality may be extended to CY 2 = K3, a setting where we cannot explicitly construct the Killing spinors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Berkovits and J. Maldacena, Fermionic T-duality dual superconformal symmetry and the amplitude/Wilson loop connection, JHEP 09 (2008) 062 [arXiv:0807.3196] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. N. Beisert, R. Ricci, A.A. Tseytlin and M. Wolf, Dual superconformal symmetry from AdS 5 × S 5 superstring integrability, Phys. Rev. D 78 (2008) 126004 [arXiv:0807.3228] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. G. Korchemsky, J. Drummond and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops, Nucl. Phys. B 795 (2008) 385 [arXiv:0707.0243] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in N = 4 super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Agarwal, N. Beisert and T. McLoughlin, Scattering in mass-deformed N ≥ 4 Chern-Simons models, JHEP 06 (2009) 045 [arXiv:0812.3367] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. T. Bargheer, F. Loebbert and C. Meneghelli, Symmetries of tree-level scattering amplitudes in N = 6 superconformal Chern-Simons theory, Phys. Rev. D 82 (2010) 045016 [arXiv:1003.6120] [INSPIRE].

    ADS  Google Scholar 

  8. S. Lee, Yangian invariant scattering amplitudes in supersymmetric Chern-Simons theory, Phys. Rev. Lett. 105 (2010) 151603 [arXiv:1007.4772] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. J.M. Henn, J. Plefka and K. Wiegandt, Light-like polygonal Wilson loops in 3D Chern-Simons and ABJM theory, JHEP 08 (2010) 032 [Erratum ibid. 1111 (2011) 053] [arXiv:1004.0226] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. Y.-t. Huang and A.E. Lipstein, Dual superconformal symmetry of N = 6 Chern-Simons theory, JHEP 11 (2010) 076 [arXiv:1008.0041] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. D. Gang, Y.-t. Huang, E. Koh, S. Lee and A.E. Lipstein, Tree-level recursion relation and dual superconformal symmetry of the ABJM theory, JHEP 03 (2011) 116 [arXiv:1012.5032] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. M.S. Bianchi, M. Leoni, A. Mauri, S. Penati, C.A. Ratti and A. Santambrogio, From correlators to Wilson loops in Chern-Simons matter theories, JHEP 06 (2011) 118 [arXiv:1103.3675] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. M.S. Bianchi, M. Leoni, A. Mauri, S. Penati and A. Santambrogio, Scattering amplitudes/Wilson loop duality in ABJM theory, JHEP 01 (2012) 056 [arXiv:1107.3139] [INSPIRE].

    Article  ADS  Google Scholar 

  14. W.-M. Chen and Y.-t. Huang, Dualities for loop amplitudes of N = 6 Chern-Simons matter theory, JHEP 11 (2011) 057 [arXiv:1107.2710] [INSPIRE].

    Article  ADS  Google Scholar 

  15. M.S. Bianchi, M. Leoni, A. Mauri, S. Penati and A. Santambrogio, Scattering in ABJ theories, JHEP 12 (2011) 073 [arXiv:1110.0738] [INSPIRE].

    Article  ADS  Google Scholar 

  16. K. Wiegandt, Equivalence of Wilson loops in \(\mathcal{N} = 6\) super Chern-Simons matter theory and \(\mathcal{N} = 4\) SYM theory, Phys. Rev. D 84(2011) 126015 [arXiv:1110.1373][INSPIRE].

    ADS  Google Scholar 

  17. M.S. Bianchi, M. Leoni and S. Penati, An all order identity between ABJM and N = 4 SYM four-point amplitudes, arXiv:1112.3649 [INSPIRE].

  18. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. I. Bakhmatov, E.O. Colgain and H. Yavartanoo, Fermionic T-duality in the PP-wave limit, JHEP 10 (2011) 085 [arXiv:1109.1052] [INSPIRE].

    Article  ADS  Google Scholar 

  20. I. Bakhmatov and D.S. Berman, Exploring fermionic T-duality, Nucl. Phys. B 832 (2010) 89 [arXiv:0912.3657] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. I. Adam, A. Dekel and Y. Oz, On integrable backgrounds self-dual under fermionic T-duality, JHEP 04 (2009) 120 [arXiv:0902.3805] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. P.A. Grassi, D. Sorokin and L. Wulff, Simplifying superstring and D-brane actions in AdS 4 × CP 3 superbackground, JHEP 08 (2009) 060 [arXiv:0903.5407] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. I. Adam, A. Dekel and Y. Oz, On the fermionic T-duality of the AdS 4 × CP 3 σ-model, JHEP 10 (2010) 110 [arXiv:1008.0649] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. I. Bakhmatov, On AdS 4 × CP 3 T-duality, Nucl. Phys. B 847 (2011) 38 [arXiv:1011.0985] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. A. Dekel and Y. Oz, Self-Duality of Green-Schwarz σ-models, JHEP 03 (2011) 117 [arXiv:1101.0400] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. T. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. K. Sfetsos, K. Siampos and D.C. Thompson, Canonical pure spinor (fermionic) T-duality, Class. Quant. Grav. 28 (2011) 055010 [arXiv:1007.5142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. H. Godazgar and M.J. Perry, Real fermionic symmetry in type-II supergravity, JHEP 01 (2011) 032 [arXiv:1008.3128] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. E. Chang-Young, H. Nakajima and H. Shin, Fermionic T-duality and Morita equivalence, JHEP 06 (2011) 002 [arXiv:1101.0473] [INSPIRE].

    Article  ADS  Google Scholar 

  30. P. Grassi and A. Mezzalira, Aspects of quantum fermionic T-duality, JHEP 05 (2011) 019 [arXiv:1101.5969] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. B. Nikolic and B. Sazdovic, Dirichlet boundary conditions in type IIB superstring theory and fermionic T-duality, arXiv:1202.0170 [INSPIRE].

  32. C. Hull, Timelike t duality, de Sitter space, large-N gauge theories and topological field theory, JHEP 07 (1998) 021 [hep-th/9806146] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. J.M. Figueroa-O’Farrill, On the supersymmetries of Anti-de Sitter vacua, Class. Quant. Grav. 16 (1999) 2043 [hep-th/9902066] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. H. Lü and Z.-L. Wang, Pseudo-Killing spinors, pseudo-supersymmetric p-branes, bubbling and less-bubbling AdS spaces, JHEP 06 (2011) 113 [arXiv:1103.0563] [INSPIRE].

    Article  ADS  Google Scholar 

  35. 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].

    Article  MathSciNet  ADS  Google Scholar 

  36. 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].

    Article  ADS  Google Scholar 

  37. J.P. Gauntlett and O.A. Mac Conamhna, AdS spacetimes from wrapped D3-branes, Class. Quant. Grav. 24 (2007) 6267 [arXiv:0707.3105] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. P.S. Aspinwall, K3 surfaces and string duality, in Differential geometry inspired by string theory, S.T. Yau ed., International Press of Boston, Boston U.S.A. (1999) 1. [hep-th/9611137] [INSPIRE].

    Google Scholar 

  39. J. Raeymaekers and K. Yogendran, Supersymmetric D-branes in the D1-D5 background, JHEP 12 (2006) 022 [hep-th/0607150] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. S. Hassan, T duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. M. Graña, D3-brane action in a supergravity background: the fermionic story, Phys. Rev. D 66 (2002) 045014 [hep-th/0202118] [INSPIRE].

    ADS  Google Scholar 

  42. H. Lü, C. Pope and J. Rahmfeld, A construction of Killing spinors on S n, J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. J.H. Schwarz, Covariant field equations of chiral N = 2 D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].

    Article  ADS  Google Scholar 

  44. O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. T. Ortín, SL(2, R) duality covariance of Killing spinors in axion - dilaton black holes, Phys. Rev. D 51 (1995) 790 [hep-th/9404035] [INSPIRE].

    ADS  Google Scholar 

  46. C. Hull and P. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. M. Sohnius, Introducing supersymmetry, Phys. Rept. 128 (1985) 39 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad de Oviedo, 33007, Oviedo, Spain

    Eoin Ó Colgáin

Authors
  1. Eoin Ó Colgáin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eoin Ó Colgáin.

Additional information

ArXiv ePrint: 1202.3416

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colgáin, E.Ó. Self-duality of the D1-D5 near-horizon. J. High Energ. Phys. 2012, 47 (2012). https://doi.org/10.1007/JHEP04(2012)047

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2012)047

Keywords

Search

Navigation