Skip to main content
SpringerLink
Account
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

BPS solutions of six-dimensional (1, 0) supergravity coupled to tensor multiplets

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 05 June 2018
  • Volume 2018, article number 21, (2018)
  • Cite this article
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
BPS solutions of six-dimensional (1, 0) supergravity coupled to tensor multiplets
Download PDF
  • Huibert het Lam  ORCID: orcid.org/0000-0001-7519-88571 &
  • Stefan Vandoren1 

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

A preprint version of the article is available at arXiv.

Abstract

We derive a general local form for supersymmetric solutions of six-dimensional (1, 0) supergravity coupled to an arbitrary number of tensor multiplets. We consider some special cases in which the resulting equations can be solved explicitly. In particular we derive black string solutions and calculate their entropy. Upon reducing to five dimensions they yield spinning black hole solutions. We also discuss BPS pp-waves and black string solutions with traveling waves. Lastly, as an application, we study the attractor mechanism in this theory.

Article PDF

Download to read the full article text

Similar content being viewed by others

Black string first order flow in N = 2, d = 5 abelian gauged supergravity

Article Open access 25 January 2017

New BPS solitons in \( \mathcal{N} \) = 4 gauged supergravity and black holes in Einstein-Yang-Mills-dilaton theory

Article Open access 08 February 2022

Conformal symmetries for extremal black holes with general asymptotic scalars in STU supergravity

Article Open access 28 September 2021
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. R. Emparan and H.S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].

    Article  MATH  Google Scholar 

  2. H.K. Kunduri and J. Lucietti, Classification of near-horizon geometries of extremal black holes, Living Rev. Rel. 16 (2013) 8 [arXiv:1306.2517] [INSPIRE].

    Article  MATH  Google Scholar 

  3. R. Emparan and H.S. Reall, A rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  4. H.K. Kunduri and J. Lucietti, Supersymmetric Black Holes with Lens-Space Topology, Phys. Rev. Lett. 113 (2014) 211101 [arXiv:1408.6083] [INSPIRE].

    Article  ADS  Google Scholar 

  5. H.K. Kunduri and J. Lucietti, Black lenses in string theory, Phys. Rev. D 94 (2016) 064007 [arXiv:1605.01545] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  6. S. Tomizawa and M. Nozawa, Supersymmetric black lenses in five dimensions, Phys. Rev. D 94 (2016) 044037 [arXiv:1606.06643] [INSPIRE].

  7. J.B. Gutowski, D. Martelli and H.S. Reall, All supersymmetric solutions of minimal supergravity in six dimensions, Class. Quant. Grav. 20 (2003) 5049 [hep-th/0306235] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. M. Akyol and G. Papadopoulos, Topology and geometry of 6-dimensional (1,0) supergravity black hole horizons, Class. Quant. Grav. 29 (2012) 055002 [arXiv:1109.4254] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391 (1997) 93 [hep-th/9602065] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. I. Bena, S. Giusto, M. Shigemori and N.P. Warner, Supersymmetric Solutions in Six Dimensions: A Linear Structure, JHEP 03 (2012) 084 [arXiv:1110.2781] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. B.E. Niehoff and N.P. Warner, Doubly-Fluctuating BPS Solutions in Six Dimensions, JHEP 10 (2013) 137 [arXiv:1303.5449] [INSPIRE].

  13. S. Giusto, L. Martucci, M. Petrini and R. Russo, 6D microstate geometries from 10D structures, Nucl. Phys. B 876 (2013) 509 [arXiv:1306.1745] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. P. de Lange, D.R. Mayerson and B. Vercnocke, Structure of Six-Dimensional Microstate Geometries, JHEP 09 (2015) 075 [arXiv:1504.07987] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  16. I. Bena et al., Asymptotically-flat supergravity solutions deep inside the black-hole regime, JHEP 02 (2018) 014 [arXiv:1711.10474] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  17. M. Cariglia and O.A.P. Mac Conamhna, The general form of supersymmetric solutions of N = (1,0) U(1) and SU(2) gauged supergravities in six-dimensions, Class. Quant. Grav. 21 (2004) 3171 [hep-th/0402055] [INSPIRE].

  18. D. Martelli and J.F. Morales, Bubbling AdS 3, JHEP 02 (2005) 048 [hep-th/0412136] [INSPIRE].

    Article  ADS  Google Scholar 

  19. N. Bobev, B.E. Niehoff and N.P. Warner, New Supersymmetric Bubbles on AdS 3 × S 3, JHEP 10 (2012) 013 [arXiv:1204.1972] [INSPIRE].

  20. B.E. Niehoff, O. Vasilakis and N.P. Warner, Multi-Superthreads and Supersheets, JHEP 04 (2013) 046 [arXiv:1203.1348] [INSPIRE].

  21. C. Vafa, Black holes and Calabi-Yau threefolds, Adv. Theor. Math. Phys. 2 (1998) 207 [hep-th/9711067] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  22. B. Haghighat, S. Murthy, C. Vafa and S. Vandoren, F-Theory, Spinning Black Holes and Multi-string Branches, JHEP 01 (2016) 009 [arXiv:1509.00455] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  23. C. Lawrie, S. Schäfer-Nameki and T. Weigand, Chiral 2d theories from N = 4 SYM with varying coupling, JHEP 04 (2017) 111 [arXiv:1612.05640] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. C. Couzens, C. Lawrie, D. Martelli, S. Schäfer-Nameki and J.-M. Wong, F-theory and AdS 3 /CFT 2, JHEP 08 (2017) 043 [arXiv:1705.04679] [INSPIRE].

    Article  ADS  Google Scholar 

  25. C. Couzens, D. Martelli and S. Schäfer-Nameki, F-theory and AdS 3 /CFT 2 (2, 0), arXiv:1712.07631 [INSPIRE].

  26. C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].

  27. D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 1, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].

  28. D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].

  29. F. Bonetti and T.W. Grimm, Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds, JHEP 05 (2012) 019 [arXiv:1112.1082] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. F. Bonetti, T.W. Grimm and S. Hohenegger, One-loop Chern-Simons terms in five dimensions, JHEP 07 (2013) 043 [arXiv:1302.2918] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. G.W. Gibbons and C.M. Hull, A Bogomolny Bound for General Relativity and Solitons in N = 2 Supergravity, Phys. Lett. B 109 (1982) 190 [INSPIRE].

  32. K.p. Tod, All Metrics Admitting Supercovariantly Constant Spinors, Phys. Lett. B 121 (1983) 241 [INSPIRE].

  33. K.P. Tod, More on supercovariantly constant spinors, Class. Quant. Grav. 12 (1995) 1801 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. P. Meessen and T. Ortín, The supersymmetric configurations of N = 2, D = 4 supergravity coupled to vector supermultiplets, Nucl. Phys. B 749 (2006) 291 [hep-th/0603099] [INSPIRE].

  36. M. Huebscher, P. Meessen and T. Ortín, Supersymmetric solutions of N = 2 D = 4 SUGRA: The whole ungauged shebang, Nucl. Phys. B 759 (2006) 228 [hep-th/0606281] [INSPIRE].

  37. J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. J.P. Gauntlett and J.B. Gutowski, All supersymmetric solutions of minimal gauged supergravity in five dimensions, Phys. Rev. D 68 (2003) 105009 [Erratum ibid. D 70 (2004) 089901] [hep-th/0304064] [INSPIRE].

  39. J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].

    Article  ADS  Google Scholar 

  40. J. Bellorín, P. Meessen and T. Ortín, All the supersymmetric solutions of N = 1, d = 5 ungauged supergravity, JHEP 01 (2007) 020 [hep-th/0610196] [INSPIRE].

  41. M. Akyol and G. Papadopoulos, Spinorial geometry and Killing spinor equations of 6D supergravity, Class. Quant. Grav. 28 (2011) 105001 [arXiv:1010.2632] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. G.W. Gibbons and S.W. Hawking, Gravitational Multi-Instantons, Phys. Lett. B 78 (1978) 430 [INSPIRE].

    Article  ADS  Google Scholar 

  43. P.M. Crichigno, F. Porri and S. Vandoren, Bound states of spinning black holes in five dimensions, JHEP 05 (2017) 101 [arXiv:1603.09729] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) R5412 [hep-th/9508072] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  45. S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  46. L. Andrianopoli, S. Ferrara, A. Marrani and M. Trigiante, Non-BPS Attractors in 5d and 6d Extended Supergravity, Nucl. Phys. B 795 (2008) 428 [arXiv:0709.3488] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  47. S. Ferrara, A. Marrani, J.F. Morales and H. Samtleben, Intersecting Attractors, Phys. Rev. D 79 (2009) 065031 [arXiv:0812.0050] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  48. A. de Antonio Martin, T. Ortín and C.S. Shahbazi, The FGK formalism for black p-branes in d dimensions, JHEP 05 (2012) 045 [arXiv:1203.0260] [INSPIRE].

  49. P.A. Cano and T. Ortín, All the supersymmetric solutions of ungauged \( \mathcal{N}=\left(1,0\right) \) , d = 6 supergravity, arXiv:1804.04945 [INSPIRE].

  50. L.J. Romans, Selfduality for Interacting Fields: Covariant Field Equations for Six-dimensional Chiral Supergravities, Nucl. Phys. B 276 (1986) 71 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  51. A. Sagnotti, A note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].

  52. S. Ferrara, F. Riccioni and A. Sagnotti, Tensor and vector multiplets in six-dimensional supergravity, Nucl. Phys. B 519 (1998) 115 [hep-th/9711059] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. P. Pasti, D.P. Sorokin and M. Tonin, On Lorentz invariant actions for chiral p forms, Phys. Rev. D 55 (1997) 6292 [hep-th/9611100] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  54. G. Dall’Agata, K. Lechner and M. Tonin, Covariant actions for N = 1, D = 6 supergravity theories with chiral bosons, Nucl. Phys. B 512 (1998) 179 [hep-th/9710127] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. J. Ford, S. Giusto and A. Saxena, A class of BPS time-dependent 3-charge microstates from spectral flow, Nucl. Phys. B 790 (2008) 258 [hep-th/0612227] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  56. O. Lunin, S.D. Mathur and D. Turton, Adding momentum to supersymmetric geometries, Nucl. Phys. B 868 (2013) 383 [arXiv:1208.1770] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. M. Shigemori, Perturbative 3-charge microstate geometries in six dimensions, JHEP 10 (2013) 169 [arXiv:1307.3115] [INSPIRE].

  58. M. Günaydin, G. Sierra and P.K. Townsend, The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  59. J.P. Gauntlett and J.B. Gutowski, General concentric black rings, Phys. Rev. D 71 (2005) 045002 [hep-th/0408122] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  60. G.W. Gibbons and P.J. Ruback, The Hidden Symmetries of Multicenter Metrics, Commun. Math. Phys. 115 (1988) 267 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  61. I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].

  62. I. Bena, N. Bobev and N.P. Warner, Spectral Flow and the Spectrum of Multi-Center Solutions, Phys. Rev. D 77 (2008) 125025 [arXiv:0803.1203] [INSPIRE].

    ADS  Google Scholar 

  63. I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].

  64. I. Bena, D.-E. Diaconescu and B. Florea, Black string entropy and Fourier-Mukai transform, JHEP 04 (2007) 045 [hep-th/0610068] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  65. J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].

  66. H. het Lam and S. Vandoren, work in progress.

  67. H. Elvang, R. Emparan, D. Mateos and H.S. Reall, A supersymmetric black ring, Phys. Rev. Lett. 93 (2004) 211302 [hep-th/0407065] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  68. H. Elvang, R. Emparan, D. Mateos and H.S. Reall, Supersymmetric black rings and three-charge supertubes, Phys. Rev. D 71 (2005) 024033 [hep-th/0408120] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  69. G.T. Horowitz and D. Marolf, Counting states of black strings with traveling waves, Phys. Rev. D 55 (1997) 835 [hep-th/9605224] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  70. G.T. Horowitz and D. Marolf, Counting states of black strings with traveling waves. 2, Phys. Rev. D 55 (1997) 846 [hep-th/9606113] [INSPIRE].

  71. N. Kaloper, R.C. Myers and H. Roussel, Wavy strings: Black or bright?, Phys. Rev. D 55 (1997) 7625 [hep-th/9612248] [INSPIRE].

  72. G.T. Horowitz and H.-s. Yang, Black strings and classical hair, Phys. Rev. D 55 (1997) 7618 [hep-th/9701077] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  73. S.F. Ross, Singularities in wavy strings, JHEP 08 (1998) 003 [hep-th/9710158] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. P. Kraus and F. Larsen, Attractors and black rings, Phys. Rev. D 72 (2005) 024010 [hep-th/0503219] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  75. S. Ferrara, R. Minasian and A. Sagnotti, Low-energy analysis of M and F theories on Calabi-Yau threefolds, Nucl. Phys. B 474 (1996) 323 [hep-th/9604097] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics and Centre for Extreme Matter and Emergent Phenomena, Utrecht University, 3508 TD, Utrecht, The Netherlands

    Huibert het Lam & Stefan Vandoren

Authors
  1. Huibert het Lam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Vandoren
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huibert het Lam.

Additional information

ArXiv ePrint: 1804.04681

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

het Lam, H., Vandoren, S. BPS solutions of six-dimensional (1, 0) supergravity coupled to tensor multiplets. J. High Energ. Phys. 2018, 21 (2018). https://doi.org/10.1007/JHEP06(2018)021

Download citation

  • Received: 24 April 2018

  • Accepted: 22 May 2018

  • Published: 05 June 2018

  • DOI: https://doi.org/10.1007/JHEP06(2018)021

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Supersymmetric Effective Theories
  • Supergravity Models
  • Black Holes
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Cancel contracts here

Not affiliated

Springer Nature

© 2024 Springer Nature