T-duality equivalences beyond string theory

  • José D. EdelsteinEmail author
  • Konstantinos Sfetsos
  • J. Anibal Sierra-Garcia
  • Alejandro Vilar López
Open Access
Regular Article - Theoretical Physics


We examine a two parameter family of gravitational actions which contains higher-derivative terms. These are such that the entire action is invariant under corrected T-duality rules, which we derive explicitly. Generically this action does not describe low energy string backgrounds except for isolated choices for the parameters. Nevertheless, we demonstrate that in this theory the entropy and the temperature of generic non-extremal black hole solutions are T-duality invariant. This further supports the idea put forward in our previous work that T-duality might provide physical equivalences beyond the realm of string theory.


String Duality Black Holes Space-Time Symmetries 


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.


  1. [1]
    J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
  2. [2]
    S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
  3. [3]
    G.T. Horowitz and D.L. Welch, Duality invariance of the Hawking temperature and entropy, Phys. Rev. D 49 (1994) 590 [hep-th/9308077] [INSPIRE].
  4. [4]
    O. Hohm and B. Zwiebach, T-duality Constraints on Higher Derivatives Revisited, JHEP 04 (2016) 101 [arXiv:1510.00005] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  5. [5]
    D. Marques and C.A. Núñez, T-duality and α -corrections, JHEP 10 (2015) 084 [arXiv:1507.00652] [INSPIRE].
  6. [6]
    O. Hohm and B. Zwiebach, Green-Schwarz mechanism and α -deformed Courant brackets, JHEP 01 (2015) 012 [arXiv:1407.0708] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    J.D. Edelstein, K. Sfetsos, J.A. Sierra-Garcia and A. Vilar López, T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm, JHEP 06 (2018) 142 [arXiv:1803.04517] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    E.A. Bergshoeff and M. de Roo, The Quartic Effective Action of the Heterotic String and Supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
  11. [11]
    O. Hohm, W. Siegel and B. Zwiebach, Doubled α -geometry, JHEP 02 (2014) 065 [arXiv:1306.2970] [INSPIRE].
  12. [12]
    R.R. Metsaev and A.A. Tseytlin, Order α (Two Loop) Equivalence of the String Equations of Motion and the σ-model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor, Nucl. Phys. B 293 (1987) 385 [INSPIRE].
  13. [13]
    G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    S.F. Hassan, T duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].
  15. [15]
    N. Kaloper and K.A. Meissner, Duality beyond the first loop, Phys. Rev. D 56 (1997) 7940 [hep-th/9705193] [INSPIRE].
  16. [16]
    T. Jacobson and A. Mohd, Black hole entropy and Lorentz-diffeomorphism Noether charge, Phys. Rev. D 92 (2015) 124010 [arXiv:1507.01054] [INSPIRE].
  17. [17]
    Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    G. Compere, An introduction to the mechanics of black holes, in 2nd Modave Summer School in Theoretical Physics, Modave, Belgium, August 6-12, 2006 (2006) [gr-qc/0611129] [INSPIRE].
  19. [19]
    V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
  20. [20]
    R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
  21. [21]
    I. Racz and R.M. Wald, Extension of space-times with Killing horizon, Class. Quant. Grav. 9 (1992) 2643 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  22. [22]
    M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
  23. [23]
    T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [gr-qc/9312023] [INSPIRE].
  24. [24]
    P.A. Cano, P. Meessen, T. Ortín and P.F. Ramírez, α′-corrected black holes in String Theory, JHEP 05 (2018) 110 [arXiv:1803.01919] [INSPIRE].
  25. [25]
    S. Chimento, P. Meessen, T. Ortín, P.F. Ramirez and A. Ruiperez, On a family of α -corrected solutions of the Heterotic Superstring effective action, JHEP 07 (2018) 080 [arXiv:1803.04463] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    A.S. Arvanitakis and C.D.A. Blair, Black hole thermodynamics, stringy dualities and double field theory, Class. Quant. Grav. 34 (2017) 055001 [arXiv:1608.04734] [INSPIRE].
  27. [27]
    J.H. Horne, G.T. Horowitz and A.R. Steif, An Equivalence between momentum and charge in string theory, Phys. Rev. Lett. 68 (1992) 568 [hep-th/9110065] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    P. Nicolini, E. Spallucci and M.F. Wondrak, Quantum Corrected Black Holes from String T-duality, arXiv:1902.11242 [INSPIRE].
  29. [29]
    E. Lescano and D. Marques, Second order higher-derivative corrections in Double Field Theory, JHEP 06 (2017) 104 [arXiv:1611.05031] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    W.H. Baron, E. Lescano and D. Marqués, The generalized Bergshoeff-de Roo identification, JHEP 11 (2018) 160 [arXiv:1810.01427] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • José D. Edelstein
    • 1
    Email author
  • Konstantinos Sfetsos
    • 2
  • J. Anibal Sierra-Garcia
    • 3
  • Alejandro Vilar López
    • 1
  1. 1.Departamento de Física de Partículas & Instituto Galego de Física de Altas Enerxías (IGFAE)Universidad de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Department of Nuclear and Particle Physics, Faculty of PhysicsNational and Kapodistrian University of AthensAthensGreece
  3. 3.Department of Physics, Faculty of ScienceChulalongkorn UniversityBangkokThailand

Personalised recommendations