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A massive class of \( \mathcal{N}=2 \) AdS4 IIA solutions

  • Achilleas Passias
  • Daniël Prins
  • Alessandro Tomasiello
Open Access
Regular Article - Theoretical Physics

Abstract

We initiate a classification of \( \mathcal{N}=2 \) supersymmetric AdS4 solutions of (massive) type IIA supergravity. The internal space is locally equipped with either an SU(2) or an identity structure. We focus on the SU(2) structure and determine the conditions it satisfies, dictated by supersymmetry. Imposing as an Ansatz that the internal space is complex, we reduce the problem of finding solutions to a Riccati ODE, which we solve analytically. We obtain in this fashion a large number of new families of solutions, both regular as well as with localized O8-planes and conical Calabi-Yau singularities. We also recover many solutions already discussed in the literature.

Keywords

AdS-CFT Correspondence Flux compactifications 

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]
    P.G.O. Freund and M.A. Rubin, Dynamics of Dimensional Reduction, Phys. Lett. B 97 (1980) 233 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    R. Corrado, K. Pilch and N.P. Warner, An N = 2 supersymmetric membrane flow, Nucl. Phys. B 629 (2002) 74 [hep-th/0107220] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M. Gabella, D. Martelli, A. Passias and J. Sparks, \( \mathcal{N}=2 \) supersymmetric AdS 4 solutions of M-theory, Commun. Math. Phys. 325 (2014) 487 [arXiv:1207.3082] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  4. [4]
    N. Halmagyi, K. Pilch and N.P. Warner, On Supersymmetric Flux Solutions of M-theory, arXiv:1207.4325 [INSPIRE].
  5. [5]
    D. Gaiotto and A. Tomasiello, The gauge dual of Romans mass, JHEP 01 (2010) 015 [arXiv:0901.0969] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States and Hierarchy, JHEP 06 (2009) 066 [arXiv:0901.0924] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    M. Petrini and A. Zaffaroni, \( \mathcal{N}=2 \) solutions of massive type IIA and their Chern-Simons duals, JHEP 09 (2009) 107 [arXiv:0904.4915] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    D. Lüst and D. Tsimpis, New supersymmetric AdS 4 type-II vacua, JHEP 09 (2009) 098 [arXiv:0906.2561] [INSPIRE].CrossRefGoogle Scholar
  9. [9]
    O. Aharony, D. Jafferis, A. Tomasiello and A. Zaffaroni, Massive type IIA string theory cannot be strongly coupled, JHEP 11 (2010) 047 [arXiv:1007.2451] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    A. Tomasiello and A. Zaffaroni, Parameter spaces of massive IIA solutions, JHEP 04 (2011) 067 [arXiv:1010.4648] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    A. Guarino, D.L. Jafferis and O. Varela, String Theory Origin of Dyonic N = 8 Supergravity and Its Chern-Simons Duals, Phys. Rev. Lett. 115 (2015) 091601 [arXiv:1504.08009] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M. Graña, R. Minasian, M. Petrini and A. Tomasiello, Generalized structures of \( \mathcal{N}=1 \) vacua, JHEP 11 (2005) 020 [hep-th/0505212] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A Scan for new \( \mathcal{N}=1 \) vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    A. Passias, G. Solard and A. Tomasiello, \( \mathcal{N}=2 \) supersymmetric AdS 4 solutions of type IIB supergravity, JHEP 04 (2018) 005 [arXiv:1709.09669] [INSPIRE].CrossRefzbMATHGoogle Scholar
  15. [15]
    A. Tomasiello, Generalized structures of ten-dimensional supersymmetric solutions, JHEP 03 (2012) 073 [arXiv:1109.2603] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    K. Behrndt, M. Cvetič and P. Gao, General type IIB fluxes with SU(3) structures, Nucl. Phys. B 721 (2005) 287 [hep-th/0502154] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    J. Bovy, D. Lüst and D. Tsimpis, N = 1, 2 supersymmetric vacua of IIA supergravity and SU(2) structures, JHEP 08 (2005) 056 [hep-th/0506160] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of M-theory, Class. Quant. Grav. 21 (2004) 4335 [hep-th/0402153] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  19. [19]
    J.P. Gauntlett, D. Martelli, J.F. Sparks and D. Waldram, A New infinite class of Sasaki-Einstein manifolds, Adv. Theor. Math. Phys. 8 (2004) 987 [hep-th/0403038] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS backgrounds in string and M-theory, IRMA Lect. Math. Theor. Phys. 8 (2005) 217 [hep-th/0411194] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  21. [21]
    W. Chen, H. Lü, C.N. Pope and J.F. Vazquez-Poritz, A Note on Einstein Sasaki metrics in D ≥ 7, Class. Quant. Grav. 22 (2005) 3421 [hep-th/0411218] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    E. Witten, Search for a Realistic Kaluza-Klein Theory, Nucl. Phys. B 186 (1981) 412 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    L. Castellani, R. D’Auria and P. Fré, SU(3) × SU(2) × U(1) from D = 11 supergravity, Nucl. Phys. B 239 (1984) 610 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    R. D’Auria, P. Fré and P. van Nieuwenhuizen, \( \mathcal{N}=2 \) Matter Coupled Supergravity From Compactification on a Coset G/H Possessing an Additional Killing Vector, Phys. Lett. B 136 (1984) 347 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    C. Couzens, D. Martelli and S. Schäfer-Nameki, F-theory and AdS 3 /CFT 2 (2, 0), JHEP 06 (2018) 008 [arXiv:1712.07631] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  26. [26]
    V. Apostolov, T. Drăghici and A. Moroianu, A splitting theorem for Kähler manifolds whose ricci tensors have constant eigenvalues, Int. J. Math. 12 (2001) 769 [math/0007122].
  27. [27]
    M. Fluder and J. Sparks, D2-brane Chern-Simons theories: F-maximization = a-maximization, JHEP 01 (2016) 048 [arXiv:1507.05817] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Achilleas Passias
    • 1
  • Daniël Prins
    • 2
    • 3
  • Alessandro Tomasiello
    • 3
  1. 1.Department of Physics and AstronomyUppsala UniversityUppsalaSweden
  2. 2.Institut de Physique Théorique, Université Paris Saclay, CNRS, CEAGif-sur-YvetteFrance
  3. 3.Dipartimento di Fisica, Università di Milano-Bicocca, and INFN, sezione di Milano-BicoccaMilanoItaly

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