Abstract
We consider the well-known solution of the Heterotic Superstring effective action to zeroth order in α′ that describes the intersection of a fundamental string with momentum and a solitonic 5-brane and which gives a 3-charge, static, extremal, supersymmetric black hole in 5 dimensions upon dimensional reduction on T5. We compute explicitly the first-order in α′ corrections to this solution, including SU(2) Yang-Mills fields which can be used to cancel some of these corrections and we study the main properties of this α′-corrected solution: supersymmetry, values of the near-horizon and asymptotic charges, behavior under α′-corrected T-duality, value of the entropy (using Wald formula directly in 10 dimensions), existence of small black holes etc. The value obtained for the entropy agrees, within the limits of approximation, with that obtained by microscopic methods. The α′ corrections coming from Wald’s formula prove crucial for this result.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038].
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].
T. Mohaupt, Black hole entropy, special geometry and strings, Fortsch. Phys. 49 (2001) 3 [hep-th/0007195] [INSPIRE].
P. Dominis Prester, α ′ -Corrections and Heterotic Black Holes, 2010, arXiv:1001.1452, http://inspirehep.net/record/842484/files/arXiv:1001.1452.pdf [INSPIRE].
A. Castro and S. Murthy, Corrections to the statistical entropy of five dimensional black holes, JHEP 06 (2009) 024 [arXiv:0807.0237] [INSPIRE].
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, arXiv:1803.04463 [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, World sheet approach to heterotic instantons and solitons, Nucl. Phys. B 359 (1991) 611 [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-Garcia and A. Vilar López, T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm, arXiv:1803.04517 [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].
E.A. Bergshoeff and M. de Roo, The Quartic Effective Action of the Heterotic String and Supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
T. Ortín, Gravity and Strings, second edition, Cambridge University Press, Cambridge U.K. (2015).
W.A. Chemissany, M. de Roo and S. Panda, α ′ -Corrections to Heterotic Superstring Effective Action Revisited, JHEP 08 (2007) 037 [arXiv:0706.3636] [INSPIRE].
E.A. Bergshoeff, R. Kallosh and T. Ortín, Supersymmetric string waves, Phys. Rev. D 47 (1993) 5444 [hep-th/9212030] [INSPIRE].
A.A. Tseytlin, Extreme dyonic black holes in string theory, Mod. Phys. Lett. A 11 (1996) 689 [hep-th/9601177] [INSPIRE].
M. Cvetič and A.A. Tseytlin, Solitonic strings and BPS saturated dyonic black holes, Phys. Rev. D 53 (1996) 5619 [Erratum ibid. D 55 (1997) 3907] [hep-th/9512031] [INSPIRE].
M.J. Duff and J.X. Lu, Elementary five-brane solutions of D = 10 supergravity, Nucl. Phys. B 354 (1991) 141 [INSPIRE].
J.M. Maldacena, Black holes in string theory, Ph.D. Thesis, Princeton University, Princeton U.S.A. (1996) [hep-th/9607235].
A.W. Peet, TASI lectures on black holes in string theory, in Proceedings of Strings, branes and gravity, TASI’99, Boulder U.S.A. (1999), J.A. Harvey, S. Kachru and E. Silverstein eds., World Scientific, New York U.S.A. (2001) [hep-th/0008241].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [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].
J. Bellorín and T. Ortín, Characterization of all the supersymmetric solutions of gauged N = 1, d = 5 supergravity, JHEP 08 (2007) 096 [arXiv:0705.2567] [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].
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].
A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167 [Erratum ibid. B 353 (1991) 565] [INSPIRE].
P.A. Cano, T. Ortín and P.F. Ramirez, A gravitating Yang-Mills instanton, JHEP 07 (2017) 011 [arXiv:1704.00504] [INSPIRE].
E. Bergshoeff and M. de Roo, Supersymmetric Chern-Simons Terms in Ten-dimensions, Phys. Lett. B 218 (1989) 210 [INSPIRE].
P. Cano, S. Chimento, P. Meessen, T. Ortín, P.F. Ramírez and A. Ruipérez, in preparation.
P.A. Cano and T. Ortín, Non-perturbative decay of Non-Abelian hair, JHEP 12 (2017) 091 [arXiv:1710.05052] [INSPIRE].
Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [INSPIRE].
A. Dabholkar, R. Kallosh and A. Maloney, A Stringy cloak for a classical singularity, JHEP 12 (2004) 059 [hep-th/0410076] [INSPIRE].
M. Alishahiha, F. Ardalan, H. Ebrahim and S. Mukhopadhyay, On 5D Small Black Holes, JHEP 03 (2008) 074 [arXiv:0712.4070] [INSPIRE].
K. Hanaki, K. Ohashi and Y. Tachikawa, Supersymmetric Completion of an R 2 term in Five-dimensional Supergravity, Prog. Theor. Phys. 117 (2007) 533 [hep-th/0611329] [INSPIRE].
N. Halmagyi, D. Israel and E.E. Svanes, The Abelian Heterotic Conifold, JHEP 07 (2016) 029 [arXiv:1601.07561] [INSPIRE].
R. Kallosh and T. Ortín, Exact SU(2) × U(1) stringy black holes, Phys. Rev. D 50 (1994) R7123 [hep-th/9409060].
B. Sahoo and A. Sen, α ′ -corrections to extremal dyonic black holes in heterotic string theory, JHEP 01 (2007) 010 [hep-th/0608182] [INSPIRE].
V. Hubeny, A. Maloney and M. Rangamani, String-corrected black holes, JHEP 05 (2005) 035 [hep-th/0411272] [INSPIRE].
K.K. Uhlenbeck, Removable singularities in yang-mills fields, Commun. Math. Phys. 83 (1982) 11 [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: 1803.01919
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., Meessen, P., Ortín, T. et al. α′-corrected black holes in String Theory. J. High Energ. Phys. 2018, 110 (2018). https://doi.org/10.1007/JHEP05(2018)110
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2018)110