Abstract
We study the first-order in α′ corrections to 4-charge black holes (with the Reissner-Nordström black hole as a particular example) beyond the near-horizon limit in the Heterotic Superstring effective action framework. The higher-curvature terms behave as delocalized sources in the equations of motion and in the Bianchi identity of the 3-form. For some charges, this introduces a shift between their values measured at the horizon and asymptotically. Some of these corrections and their associated charge shifts, but not all of them, can be canceled using appropriate SU(2) instantons for the heterotic gauge fields. The entropy, computed using Wald’s formula, is in agreement with the result obtained via microstate counting when the delocalized sources are properly taken into account.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Chimento, P. Meessen, T. Ortín, P.F. Ramírez and A. Ruipérez, On a family of α ′ -corrected solutions of the Heterotic Superstring effective action, JHEP 07 (2018) 080 [arXiv:1803.04463] [INSPIRE].
P.A. Cano, P. Meessen, T. Ortín and P.F. Ramírez, Non-Abelian black holes in string theory, JHEP 12 (2017) 092 [arXiv:1704.01134] [INSPIRE].
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].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.M. Maldacena and A. Strominger, Statistical entropy of four-dimensional extremal black holes, Phys. Rev. Lett. 77 (1996) 428 [hep-th/9603060] [INSPIRE].
C.V. Johnson, R.R. Khuri and R.C. Myers, Entropy of 4-D extremal black holes, Phys. Lett. B 378 (1996) 78 [hep-th/9603061] [INSPIRE].
J.M. Maldacena, Black holes in string theory, Ph.D. thesis, Princeton Universiy, (1996), hep-th/9607235 [INSPIRE].
P. Kraus, Lectures on black holes and the AdS 3 /CF T 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
M. Cvetič and D. Youm, Dyonic BPS saturated black holes of heterotic string on a six torus, Phys. Rev. D 53 (1996) 584 [hep-th/9507090] [INSPIRE].
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].
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].
D. Kutasov, F. Larsen and R.G. Leigh, String theory in magnetic monopole backgrounds, Nucl. Phys. B 550 (1999) 183 [hep-th/9812027] [INSPIRE].
E. Bergshoeff and M. de Roo, Supersymmetric Chern-Simons Terms in Ten-dimensions, Phys. Lett. B 218 (1989) 210 [INSPIRE].
E.A. Bergshoeff and M. de Roo, The Quartic Effective Action of the Heterotic String and Supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
A. Kehagias and H. Partouche, On the exact quartic effective action for the type IIB superstring, Phys. Lett. B 422 (1998) 109 [hep-th/9710023] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
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].
A. Sen, Entropy function for heterotic black holes, JHEP 03 (2006) 008 [hep-th/0508042] [INSPIRE].
P. Meessen, Supersymmetric coloured/hairy black holes, Phys. Lett. B 665 (2008) 388 [arXiv:0803.0684] [INSPIRE].
P. Meessen, T. Ortín and P.F. Ramírez, Non-Abelian, supersymmetric black holes and strings in 5 dimensions, JHEP 03 (2016) 112 [arXiv:1512.07131] [INSPIRE].
P.F. Ramírez, Non-Abelian bubbles in microstate geometries, JHEP 11 (2016) 152 [arXiv:1608.01330] [INSPIRE].
P.A. Cano, T. Ortın and P.F. Ramírez, A gravitating Yang-Mills instanton, JHEP 07 (2017) 011 [arXiv:1704.00504] [INSPIRE].
J. Ávila, P.F. Ramírez and A. Ruipérez, One Thousand and One Bubbles, JHEP 01 (2018) 041 [arXiv:1709.03985] [INSPIRE].
T. Ortín, Gravity and Strings, 2nd edition, Cambridge University Press, (2015).
E.A. Bergshoeff, R. Kallosh and T. Ortín, Supersymmetric string waves, Phys. Rev. D 47 (1993) 5444 [hep-th/9212030] [INSPIRE].
P.B. Kronheimer, Monopoles and Taub-NUT spaces, MSc Thesis, Oxford University, (1985).
E.B. Bogomolny, Stability of Classical Solutions, Sov. J. Nucl. Phys. 24 (1976) 449 [INSPIRE].
G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
A.M. Polyakov, Particle Spectrum in the Quantum Field Theory, JETP Lett. 20 (1974) 194 [INSPIRE].
M.K. Prasad and C.M. Sommerfield, An Exact Classical Solution for the ’t Hooft Monopole and the Julia-Zee Dyon, Phys. Rev. Lett. 35 (1975) 760 [INSPIRE].
A.P. Protogenov, Exact Classical Solutions of Yang-Mills Sourceless Equations, Phys. Lett. 67B (1977) 62 [INSPIRE].
M. Huebscher, P. Meessen, T. Ortín and S. Vaulà, Supersymmetric N = 2 Einstein-Yang-Mills monopoles and covariant attractors, Phys. Rev. D 78 (2008) 065031 [arXiv:0712.1530] [INSPIRE].
M. Huebscher, P. Meessen, T. Ortín and S. Vaulà, N = 2 Einstein-Yang-Mills’s BPS solutions, JHEP 09 (2008) 099 [arXiv:0806.1477] [INSPIRE].
P. Bueno, P. Meessen, T. Ortín and P.F. Ramírez, \( \mathcal{N}=2 \) Einstein-Yang-Mills’ static two-center solutions, JHEP 12 (2014) 093 [arXiv:1410.4160] [INSPIRE].
P. Meessen and T. Ortín, \( \mathcal{N}=2 \) super-EYM coloured black holes from defective Lax matrices, JHEP 04 (2015) 100 [arXiv:1501.02078] [INSPIRE].
P. Bueno, P. Meessen, T. Ortín and P.F. Ramírez, Resolution of SU(2) monopole singularities by oxidation, Phys. Lett. B 746 (2015) 109 [arXiv:1503.01044] [INSPIRE].
A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Yu.S. Tyupkin, Pseudoparticle Solutions of the Yang-Mills Equations, Phys. Lett. B 59 (1975) 85 [INSPIRE].
J. Bellorın and T. Ortín, Characterization of all the supersymmetric solutions of gauged N = 1, d = 5 supergravity, JHEP 08 (2007) 096 [arXiv:0705.2567] [INSPIRE].
A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167 [Erratum ibid. B 353 (1991) 565] [INSPIRE].
T.T. Wu and C.-N. Yang, Some Solutions Of The Classical Isotopic Gauge Field Equations, in Yang, C.N.: Selected Papers 1945-1980, pp. 400-405 also in H. Mark and S. Fernbach, Properties Of Matter Under Unusual Conditions, New York, U.S.A. (1969), pp. 349-345.
H. Boutaleb-Joutei, A. Chakrabarti and A. Comtet, Gauge Field Configurations in Curved Space-times. 5. Regularity Constraints and Quantized Actions, Phys. Rev. D 21 (1980) 2285 [INSPIRE].
H. Boutaleb-Joutei, A. Chakrabarti and A. Comtet, Gauge Field Configurations in Curved Space-times. 4. Selfdual SU(2) Fields in Multicenter Spaces, Phys. Rev. D 21 (1980) 2280 [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, Supersymmetric string solitons, hep-th/9112030 [INSPIRE].
E. Bergshoeff, B. Janssen and T. Ortín, Solution generating transformations and the string effective action, Class. Quant. Grav. 13 (1996) 321 [hep-th/9506156] [INSPIRE].
J.D. Edelstein, K. Sfetsos, J.A. Sierra-García 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].
P.A. Cano and T. Ortín, Non-perturbative decay of Non-Abelian hair, JHEP 12 (2017) 091 [arXiv:1710.05052] [INSPIRE].
M.J. Duff, R.R. Khuri and J.X. Lu, String solitons, Phys. Rept. 259 (1995) 213 [hep-th/9412184] [INSPIRE].
P. Cano, P.F. Ramírez and A. Ruipérez, in preparation.
P.A. Cano, S. Chimento, T. Ortín and A. Ruipérez, Regular Stringy Black Holes?, arXiv:1806.08377 [INSPIRE].
P. Dominis Prester and T. Terzic, α ′ -exact entropies for BPS and non-BPS extremal dyonic black holes in heterotic string theory from ten-dimensional supersymmetry, JHEP 12 (2008) 088 [arXiv:0809.4954] [INSPIRE].
P. Dominis Prester, α ′ -Corrections and Heterotic Black Holes, arXiv:1001.1452 [INSPIRE].
P.A. Cano, P.F. Ramírez and A. Ruipérez, The small black hole illusion, arXiv:1808.10449 [INSPIRE].
A. Castro and S. Murthy, Corrections to the statistical entropy of five dimensional black holes, JHEP 06 (2009) 024 [arXiv:0807.0237] [INSPIRE].
A. Castro, J.L. Davis, P. Kraus and F. Larsen, String Theory Effects on Five-Dimensional Black Hole Physics, Int. J. Mod. Phys. A 23 (2008) 613 [arXiv:0801.1863] [INSPIRE].
A. Sen, Kaluza-Klein dyons in string theory, Phys. Rev. Lett. 79 (1997) 1619 [hep-th/9705212] [INSPIRE].
A. Sen, Dynamics of multiple Kaluza-Klein monopoles in M and string theory, Adv. Theor. Math. Phys. 1 (1998) 115 [hep-th/9707042] [INSPIRE].
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
Corresponding author
Additional information
ArXiv ePrint: 1808.03651
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/.
About this article
Cite this article
Cano, P.A., Chimento, S., Meessen, P. et al. Beyond the near-horizon limit: stringy corrections to heterotic black holes. J. High Energ. Phys. 2019, 192 (2019). https://doi.org/10.1007/JHEP02(2019)192
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2019)192