Advertisement

Field theory aspects of non-Abelian T-duality and \( \mathcal{N} \) =2 linear quivers

  • Yolanda Lozano
  • Carlos Núñez
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS 5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d \( \mathcal{N} \) = 2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Núñez. This suggests different completions of the long quiver describing the CFT dual to the nonAbelian T-dual background that match different observables.

Keywords

AdS-CFT Correspondence String Duality Gauge-gravity correspondence 

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]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    X.C. de la Ossa and F. Quevedo, Duality symmetries from non-Abelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  5. [5]
    A. Giveon and M. Roček, On non-Abelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    E. Alvarez, L. Álvarez-Gaumé, J.L.F. Barbon and Y. Lozano, Some global aspects of duality in string theory, Nucl. Phys. B 415 (1994) 71 [hep-th/9309039] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-Abelian T-duality, Ramondfields and coset geometries, JHEP 06 (2011) 106 [arXiv:1104.5196] [INSPIRE].
  9. [9]
    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].
  10. [10]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Y. Lozano, E. Ó Colgáin, D. Rodríguez-Gómez and K. Sfetsos, Supersymmetric AdS6 via T duality, Phys. Rev. Lett. 110 (2013) 231601 [arXiv:1212.1043] [INSPIRE].
  12. [12]
    G. Itsios, C. Núñez, K. Sfetsos and D.C. Thompson, On non-Abelian T-duality and new N =1 backgrounds, Phys. Lett. B 721 (2013) 342 [arXiv:1212.4840] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    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].
  14. [14]
    A. Barranco, J. Gaillard, N.T. Macpherson, C. Núñez and D.C. Thompson, G-structures and flavouring non-Abelian T-duality, JHEP 08 (2013) 018 [arXiv:1305.7229] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    N.T. Macpherson, Non-Abelian T-duality, G 2 -structure rotation and holographic duals of N =1 Chern-Simons theories, JHEP 11 (2013) 137 [arXiv:1310.1609] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    J. Gaillard, N.T. Macpherson, C. Núñez and D.C. Thompson, Dualising the baryonic branch: dynamic SU(2) and confining backgrounds in IIA, Nucl. Phys. B 884 (2014) 696 [arXiv:1312.4945] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  17. [17]
    D. Elander, A.F. Faedo, C. Hoyos, D. Mateos and M. Piai, Multiscale confining dynamics from holographic RG flows, JHEP 05 (2014) 003 [arXiv:1312.7160] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    S. Zacarías, Semiclassical strings and non-Abelian T-duality, Phys. Lett. B 737 (2014) 90 [arXiv:1401.7618] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    E. Caceres, N.T. Macpherson and C. Núñez, New type IIB backgrounds and aspects of their field theory duals, JHEP 08 (2014) 107 [arXiv:1402.3294] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    P.M. Pradhan, Oscillating strings and non-Abelian T-dual Klebanov-Witten background, Phys. Rev. D 90 (2014) 046003 [arXiv:1406.2152] [INSPIRE].ADSGoogle Scholar
  21. [21]
    K. Sfetsos and D.C. Thompson, New N = 1 supersymmetric AdS 5 backgrounds in type IIA supergravity, JHEP 11 (2014) 006 [arXiv:1408.6545] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    L.A.P. Zayas, V.G.J. Rodgers and C.A. Whiting, Supergravity solutions with AdS 4 from non-Abelian T-dualities, JHEP 02 (2016) 061 [arXiv:1511.05991] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    H. Dimov, S. Mladenov, R.C. Rashkov and T. Vetsov, Non-Abelian T-duality of Pilch-Warner background, arXiv:1511.00269 [INSPIRE].
  24. [24]
    Ö. Kelekci, Y. Lozano, N.T. Macpherson and E. Ó. Colgáin, Supersymmetry and non-Abelian T-duality in type-II supergravity, Class. Quant. Grav. 32 (2015) 035014 [arXiv:1409.7406] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    K.S. Kooner and S. Zacarías, Non-Abelian T-dualizing the resolved conifold with regular and fractional D3-branes, JHEP 08 (2015) 143 [arXiv:1411.7433] [INSPIRE].
  26. [26]
    T.R. Araujo and H. Nastase, N = 1 SUSY backgrounds with an AdS factor from non-Abelian T duality, Phys. Rev. D 91 (2015) 126015 [arXiv:1503.00553] [INSPIRE].ADSMathSciNetGoogle Scholar
  27. [27]
    Y. Lozano, N.T. Macpherson, J. Montero and E. Ó. Colgáin, New AdS 3 × S 2 T-duals with N =(0,4) supersymmetry, JHEP 08 (2015) 121 [arXiv:1507.02659] [INSPIRE].
  28. [28]
    T.R. Araujo and H. Nastase, Non-Abelian T-duality for nonrelativistic holographic duals, JHEP 11 (2015) 203 [arXiv:1508.06568] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    Y. Lozano, N.T. Macpherson and J. Montero, A N = 2 supersymmetric AdS 4 solution in M-theory with purely magnetic flux, JHEP 10 (2015) 004 [arXiv:1507.02660] [INSPIRE].ADSMathSciNetGoogle Scholar
  30. [30]
    N.T. Macpherson, C. Núñez, L.A. Pando Zayas, V.G.J. Rodgers and C.A. Whiting, Type IIB supergravity solutions with AdS 5 from Abelian and non-Abelian T dualities, JHEP 02 (2015) 040 [arXiv:1410.2650] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    Y. Lozano, E. Ó Colgáin and D. Rodríguez-Gómez, Hints of 5d fixed point theories from non-Abelian T-duality, JHEP 05 (2014) 009 [arXiv:1311.4842] [INSPIRE].
  32. [32]
    Y. Lozano and N.T. Macpherson, A new AdS 4 /CF T 3 dual with extended SUSY and a spectral flow, JHEP 11 (2014) 115 [arXiv:1408.0912] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    N.T. Macpherson, C. Núñez, D.C. Thompson and S. Zacarias, Holographic flows in non-Abelian T-dual geometries, JHEP 11 (2015) 212 [arXiv:1509.04286] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005] [INSPIRE].
  37. [37]
    N. Arkani-Hamed, A.G. Cohen, D.B. Kaplan, A. Karch and L. Motl, Deconstructing (2, 0) and little string theories, JHEP 01 (2003) 083 [hep-th/0110146] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  38. [38]
    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].
  39. [39]
    A. Fayyazuddin and D.J. Smith, Localized intersections of M 5-branes and four-dimensional superconformal field theories, JHEP 04 (1999) 030 [hep-th/9902210] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  42. [42]
    M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].ADSMathSciNetGoogle Scholar
  43. [43]
    M. Alishahiha and Y. Oz, AdS/CFT and BPS strings in four-dimensions, Phys. Lett. B 465 (1999) 136 [hep-th/9907206] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    Y. Lozano, J. Montero and C. Núñez, in progress.Google Scholar
  45. [45]
    A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  46. [46]
    R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    R.A. Reid-Edwards and B. Stefanski Jr., On type IIA geometries dual to N = 2 SCFTs, Nucl. Phys. B 849 (2011) 549 [arXiv:1011.0216] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  49. [49]
    O. Aharony, L. Berdichevsky and M. Berkooz, 4d N = 2 superconformal linear quivers with type IIA duals, JHEP 08 (2012) 131 [arXiv:1206.5916] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  51. [51]
    I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  52. [52]
    Y. Bea et al., Compactifications of the Klebanov-Witten CFT and new AdS 3 backgrounds, JHEP 05 (2015) 062 [arXiv:1503.07527] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    A.D. Shapere and Y. Tachikawa, Central charges of N = 2 superconformal field theories in four dimensions, JHEP 09 (2008) 109 [arXiv:0804.1957] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  54. [54]
    U. Kol, C. Núñez, D. Schofield, J. Sonnenschein and M. Warschawski, Confinement, phase transitions and non-locality in the entanglement entropy, JHEP 06 (2014) 005 [arXiv:1403.2721] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, Deconstructing (2, 0) proposals, Phys. Rev. D 88 (2013) 026007 [arXiv:1212.3337] [INSPIRE].ADSGoogle Scholar
  56. [56]
    K. Sfetsos, Dynamical emergence of extra dimensions and warped geometries, Nucl. Phys. B 612 (2001) 191 [hep-th/0106126] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  57. [57]
    A.P. Polychronakos and K. Sfetsos, High spin limits and non-Abelian T-duality, Nucl. Phys. B 843 (2011) 344 [arXiv:1008.3909] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  58. [58]
    D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, JHEP 12 (2014) 003 [arXiv:1404.0711] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    S. Cremonesi and A. Tomasiello, 6d holographic anomaly match as a continuum limit, JHEP 05 (2016) 031 [arXiv:1512.02225] [INSPIRE].CrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of OviedoOviedoSpain
  2. 2.Department of PhysicsSwansea UniversitySwanseaU.K.

Personalised recommendations