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Journal of High Energy Physics

, 2014:152 | Cite as

Order α′ heterotic domain walls with warped nearly Kähler geometry

  • Alexander S. Haupt
  • Olaf LechtenfeldEmail author
  • Edvard T. Musaev
Open Access
Regular Article - Theoretical Physics

Abstract

We consider (1+3)-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kähler manifold X 6 in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [1]. We include first order α′ corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present a variety of solutions, depending on the choice of instantons, for the special case in which the SU(3) structure on X 6 satisfies \( {W}_{\overline{1}}=0 \). The solutions preserve two real supercharges, which corresponds to \( \mathcal{N}=1/2 \) supersymmetry from the four-dimensional point of view. Besides serving as a useful framework for collecting existing solutions, the formulation in terms of dynamic SU(3) structures utilized here allows us to obtain new solutions in as yet unexplored corners of the instanton configuration space. Our approach thus offers a unified description of the embedding of tanh-kink-type instantons into half-BPS solutions of heterotic supergravity where the internal six-dimensional manifold has a warped nearly Kähler geometry.

Keywords

Flux compactifications Solitons Monopoles and Instantons Supergravity Models 

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]
    D. Harland and C. Nolle, Instantons and Killing spinors, JHEP 03 (2012) 082 [arXiv:1109.3552] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  2. [2]
    M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006)91 [hep-th/0509003] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    B. Wecht, Lectures on nongeometric flux compactifications, Class. Quant. Grav. 24 (2007) S773 [arXiv:0708.3984] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    H. Samtleben, Lectures on gauged supergravity and flux compactifications, Class. Quant. Grav. 25 (2008) 214002 [arXiv:0808.4076] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    F. Quevedo, Lectures on superstring phenomenology, AIP Conf. Proc. 359 (1996) 202 [hep-th/9603074] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    D. Joyce, Lectures on Calabi-Yau and special Lagrangian geometry, math/0108088 [INSPIRE].
  9. [9]
    M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, Heterotic string theory. 1. The free heterotic string, Nucl. Phys. B 256 (1985) 253 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, Heterotic string theory. 2. The interacting heterotic string, Nucl. Phys. B 267 (1986) 75 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    C.M. Hull, Anomalies, ambiguities and superstrings, Phys. Lett. B 167 (1986) 51 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    S. Ivanov, Heterotic supersymmetry, anomaly cancellation and equations of motion, Phys. Lett. B 685 (2010) 190 [arXiv:0908.2927] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    E.A. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    K. Becker and S. Sethi, Torsional heterotic geometries, Nucl. Phys. B 820 (2009) 1 [arXiv:0903.3769] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  16. [16]
    G.T. Horowitz and A. Strominger, Black strings and P-branes, Nucl. Phys. B 360 (1991) 197 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167 [Erratum ibid. B 353 (1991) 565] [INSPIRE].
  18. [18]
    J.A. Harvey and A. Strominger, Octonionic superstring solitons, Phys. Rev. Lett. 66 (1991) 549 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  19. [19]
    R.R. Khuri, Remark on string solitons, Phys. Rev. D 48 (1993) 2947 [hep-th/9305143] [INSPIRE].ADSMathSciNetGoogle Scholar
  20. [20]
    M. Günaydin and H. Nicolai, Seven-dimensional octonionic Yang-Mills instanton and its extension to an heterotic string soliton, Phys. Lett. B 351 (1995) 169 [Addendum ibid. B 376 (1996) 329] [hep-th/9502009] [INSPIRE].
  21. [21]
    E.K. Loginov, Some comments on string solitons, Phys. Rev. D 77 (2008) 105003 [arXiv:0805.0870] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    K.-P. Gemmer, A.S. Haupt, O. Lechtenfeld, C. Nölle and A.D. Popov, Heterotic string plus five-brane systems with asymptotic AdS 3, Adv. Theor. Math. Phys. 17 (2013) 771 [arXiv:1202.5046] [INSPIRE].CrossRefzbMATHMathSciNetGoogle Scholar
  23. [23]
    M. Klaput, A. Lukas, C. Matti and E.E. Svanes, Moduli stabilising in heterotic nearly Kähler compactifications, JHEP 01 (2013) 015 [arXiv:1210.5933] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    J. Gray, M. Larfors and D. Lüst, Heterotic domain wall solutions and SU(3) structure manifolds, JHEP 08 (2012) 099 [arXiv:1205.6208] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    A. Lukas and C. Matti, G-structures and domain walls in heterotic theories, JHEP 01 (2011) 151 [arXiv:1005.5302] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  26. [26]
    S. Chiossi and S. Salamon, The intrinsic torsion of SU(3) and G 2 structures, math/0202282 [INSPIRE].
  27. [27]
    N.J. Hitchin, Stable forms and special metrics, math/0107101 [INSPIRE].
  28. [28]
    C. Mayer and T. Mohaupt, Domain walls, Hitchins flow equations and G 2 -manifolds, Class. Quant. Grav. 22 (2005) 379 [hep-th/0407198] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  29. [29]
    J. Louis and S. Vaula, N = 1 domain wall solutions of massive type-II supergravity as generalized geometries, JHEP 08 (2006) 058 [hep-th/0605063] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  30. [30]
    P. Smyth and S. Vaula, Domain wall flow equations and SU(3) × SU(3) structure compactifications, Nucl. Phys. B 828 (2010) 102 [arXiv:0905.1334] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  31. [31]
    J.P. Gauntlett, D. Martelli, S. Pakis and D. Waldram, G structures and wrapped NS5-branes, Commun. Math. Phys. 247 (2004) 421 [hep-th/0205050] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  32. [32]
    D. Martelli and J. Sparks, Non-Kähler heterotic rotations, Adv. Theor. Math. Phys. 15 (2011)131 [arXiv:1010.4031] [INSPIRE].CrossRefzbMATHMathSciNetGoogle Scholar
  33. [33]
    X. de la Ossa and E.E. Svanes, Holomorphic bundles and the moduli space of N = 1 supersymmetric heterotic compactifications, JHEP 10 (2014) 123 [arXiv:1402.1725] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    M. Fernandez, S. Ivanov, L. Ugarte and D. Vassilev, Non-Kähler heterotic string solutions with non-zero fluxes and non-constant dilaton, JHEP 06 (2014) 073 [arXiv:1402.6107] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  35. [35]
    I.V. Melnikov, R. Minasian and S. Sethi, Heterotic fluxes and supersymmetry, JHEP 06 (2014) 174 [arXiv:1403.4298] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  36. [36]
    T. Maxfield and S. Sethi, Domain walls, triples and acceleration, JHEP 08 (2014) 066 [arXiv:1404.2564] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  37. [37]
    A. Gray, The structure of nearly Kähler manifolds, Math. Ann. 223 (1976) 233.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Alexander S. Haupt
    • 1
    • 2
  • Olaf Lechtenfeld
    • 1
    Email author
  • Edvard T. Musaev
    • 1
    • 3
    • 4
  1. 1.Institut für Theoretische Physik and Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany
  2. 2.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany
  3. 3.Université de Lyon, Laboratoire de Physique, UMR 5672, CNRS, École Normale Supérieure de LyonLyon CEDEX 07France
  4. 4.National Research University Higher School of Economics, Faculty of MathematicsMoscowRussia

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