Abstract
We review and extend results on higher-curvature corrections to different configurations describing a superposition of heterotic strings, KK monopoles, solitonic 5-branes and momentum waves. Depending on which sources are present, the low-energy fields describe a black hole, a soliton or a naked singularity. We show that this property is unaltered when perturbative higher-curvature corrections are included, provided the sources are fixed. On the other hand, this character may be changed by appropriate introduction (or removal) of sources regardless of the presence of curvature corrections, which constitutes a non-perturbative modification of the departing system. The general system of multicenter KK monopoles and their 5-brane charge induced by higher-curvature corrections is discussed in some detail, with special attention paid to the possibility of merging monopoles. Our results are particularly relevant for small black holes (Dabholkar-Harvey states, DH), which remain singular after quadratic curvature corrections are taken into account. When there are four non-compact dimensions, we notice the existence of a black hole with regular horizon whose entropy coincides with that of the DH states, but the charges and supersymmetry preserved by both configurations are different. A similar construction with five non-compact dimensions is possible, in this case with the same charges as DH, although it fails to reproduce the DH entropy and supersymmetry. No such configuration exists if d > 5, which we interpret as reflecting the necessity of having a 5-brane wrapping the compact space.
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References
G.T. Horowitz and R.C. Myers, The value of singularities, Gen. Rel. Grav. 27 (1995) 915 [gr-qc/9503062] [INSPIRE].
S.S. Gubser, Curvature singularities: The Good, the bad, and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
S.D. Mathur and D. Turton, The fuzzball nature of two-charge black hole microstates, Nucl. Phys. B 945 (2019) 114684 [arXiv:1811.09647] [INSPIRE].
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].
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.A. Cano and T. Ortín, The structure of all the supersymmetric solutions of ungauged \( \mathcal{N} \) = (1, 0), d = 6 supergravity, Class. Quant. Grav. 36 (2019) 125007 [arXiv:1804.04945] [INSPIRE].
R. Kallosh and T. Ortín, Killing spinor identities, hep-th/9306085 [INSPIRE].
J. Bellorín and T. Ortín, A Note on simple applications of the Killing Spinor Identities, Phys. Lett. B 616 (2005) 118 [hep-th/0501246] [INSPIRE].
T.H. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167 [Erratum ibid. 353 (1991) 565] [INSPIRE].
M.J. Duff and J.X. Lu, Strings from five-branes, Phys. Rev. Lett. 66 (1991) 1402 [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].
A. Sen, Strong-weak coupling duality in four-dimensional string theory, Int. J. Mod. Phys. A 9 (1994) 3707 [hep-th/9402002] [INSPIRE].
J.H. Schwarz, Evidence for nonperturbative string symmetries, Lett. Math. Phys. 34 (1995) 309 [hep-th/9411178] [INSPIRE].
M.J. Duff, Strong/weak coupling duality from the dual string, Nucl. Phys. B 442 (1995) 47 [hep-th/9501030] [INSPIRE].
J. Polchinski, Dirichlet Branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
J. Polchinski, TASI lectures on D-branes, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, (1996) [hep-th/9611050] [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].
J.M. Maldacena, Black holes in string theory, Ph.D. Thesis, Princeton U. (1996) [hep-th/9607235] [INSPIRE].
P. Kraus, Lectures on black holes and the AdS3/CFT2 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].
A. Sen, Extremal black holes and elementary string states, Nucl. Phys. B Proc. Suppl. 46 (1996) 198 [INSPIRE].
A. Dabholkar and J.A. Harvey, Nonrenormalization of the Superstring Tension, Phys. Rev. Lett. 63 (1989) 478 [INSPIRE].
A. Dabholkar, G.W. Gibbons, J.A. Harvey and F. Ruiz Ruiz, Superstrings and Solitons, Nucl. Phys. B 340 (1990) 33 [INSPIRE].
J.G. Russo and L. Susskind, Asymptotic level density in heterotic string theory and rotating black holes, Nucl. Phys. B 437 (1995) 611 [hep-th/9405117] [INSPIRE].
A. Sen, Black hole solutions in heterotic string theory on a torus, Nucl. Phys. B 440 (1995) 421 [hep-th/9411187] [INSPIRE].
L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].
O. Lunin and S.D. Mathur, Statistical interpretation of Bekenstein entropy for systems with a stretched horizon, Phys. Rev. Lett. 88 (2002) 211303 [hep-th/0202072] [INSPIRE].
A. Dabholkar, Exact counting of black hole microstates, Phys. Rev. Lett. 94 (2005) 241301 [hep-th/0409148] [INSPIRE].
A. Dabholkar, R. Kallosh and A. Maloney, A Stringy cloak for a classical singularity, JHEP 12 (2004) 059 [hep-th/0410076] [INSPIRE].
A. Sen, Two Charge System Revisited: Small Black Holes or Horizonless Solutions?, JHEP 05 (2010) 097 [arXiv:0908.3402] [INSPIRE].
A. Sen, How does a fundamental string stretch its horizon?, JHEP 05 (2005) 059 [hep-th/0411255] [INSPIRE].
V. Hubeny, A. Maloney and M. Rangamani, String-corrected black holes, JHEP 05 (2005) 035 [hep-th/0411272] [INSPIRE].
A. Sen, Stretching the horizon of a higher dimensional small black hole, JHEP 07 (2005) 073 [hep-th/0505122] [INSPIRE].
B. Sahoo and A. Sen, α′ -Corrections to extremal dyonic black holes in heterotic string theory, JHEP 01 (2007) 010 [hep-th/0608182] [INSPIRE].
A. Dabholkar, N. Iizuka, A. Iqubal, A. Sen and M. Shigemori, Spinning strings as small black rings, JHEP 04 (2007) 017 [hep-th/0611166] [INSPIRE].
K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press (2006) [DOI].
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, (2010) [arXiv:1001.1452] [INSPIRE].
D. Polini, Generating new N = 2 small black holes, JHEP 06 (2019) 001 [arXiv:1904.05832] [INSPIRE].
K. Behrndt, G. Lopes Cardoso, B. de Wit, D. Lüst, T. Mohaupt and W.A. Sabra, Higher order black hole solutions in N = 2 supergravity and Calabi-Yau string backgrounds, Phys. Lett. B 429 (1998) 289 [hep-th/9801081] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Deviations from the area law for supersymmetric black holes, Fortsch. Phys. 48 (2000) 49 [hep-th/9904005] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Macroscopic entropy formulae and nonholomorphic corrections for supersymmetric black holes, Nucl. Phys. B 567 (2000) 87 [hep-th/9906094] [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].
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].
P.A. Cano, S. Chimento, P. Meessen, T. Ortín, P.F. Ramírez and A. Ruipérez, Beyond the near-horizon limit: Stringy corrections to Heterotic Black Holes, JHEP 02 (2019) 192 [arXiv:1808.03651] [INSPIRE].
P.A. Cano, P.F. Ramírez and A. Ruipérez, The small black hole illusion, JHEP 03 (2020) 115 [arXiv:1808.10449] [INSPIRE].
P.A. Cano, S. Chimento, T. Ortín and A. Ruipérez, Regular Stringy Black Holes?, Phys. Rev. D 99 (2019) 046014 [arXiv:1806.08377] [INSPIRE].
F. Faedo and P.F. Ramirez, Exact charges from heterotic black holes, JHEP 10 (2019) 033 [arXiv:1906.12287] [INSPIRE].
P.A. Cano, T. Ortín and P.F. Ramirez, On the extremality bound of stringy black holes, JHEP 02 (2020) 175 [arXiv:1909.08530] [INSPIRE].
P.A. Cano, S. Chimento, R. Linares, T. Ortín and P.F. Ramírez, α′ corrections of Reissner-Nordström black holes, JHEP 02 (2020) 031 [arXiv:1910.14324] [INSPIRE].
A. Ruipérez, Higher-derivative corrections to small black rings, arXiv:2003.02269 [INSPIRE].
D.J. Gross and J.H. Sloan, The Quartic Effective Action for the Heterotic String, Nucl. Phys. B 291 (1987) 41 [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].
R.R. Metsaev and A.A. Tseytlin, Order alpha-prime (Two Loop) Equivalence of the String Equations of Motion and the Sigma Model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor, Nucl. Phys. B 293 (1987) 385 [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].
M. Cvetič and D. Youm, General rotating five-dimensional black holes of toroidally compactified heterotic string, Nucl. Phys. B 476 (1996) 118 [hep-th/9603100] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Gravitational Multi-Instantons, Phys. Lett. B 78 (1978) 430 [INSPIRE].
G.W. Gibbons and P.J. Ruback, The Hidden Symmetries of Multicenter Metrics, Commun. Math. Phys. 115 (1988) 267 [INSPIRE].
A. Sen, Kaluza-Klein dyons in string theory, Phys. Rev. Lett. 79 (1997) 1619 [hep-th/9705212] [INSPIRE].
D. Marolf, Chern-Simons terms and the three notions of charge, in International Conference on Quantization, Gauge Theory, and Strings: Conference Dedicated to the Memory of ProfeSSOR Efim Fradkin, (2000) [hep-th/0006117] [INSPIRE].
Z. Elgood and T. Ortín, T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′, JHEP 10 (2020) 097 [arXiv:2005.11272] [INSPIRE].
T. Ortín, O(n, n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in α′, JHEP 01 (2021) 187 [arXiv:2005.14618] [INSPIRE].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [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].
A. Castro and S. Murthy, Corrections to the statistical entropy of five dimensional black holes, JHEP 06 (2009) 024 [arXiv:0807.0237] [INSPIRE].
H. Nicolai and P.K. Townsend, N = 3 Supersymmetry Multiplets with Vanishing Trace Anomaly: Building Blocks of the N > 3 Supergravities, Phys. Lett. B 98 (1981) 257 [INSPIRE].
Z. Elgood, T. Ortín and D. Pereñíguez, The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime, arXiv:2012.14892 [INSPIRE].
Z. Elgood, D. Mitsios, T. Ortín and D. Pereñíguez, The first law of heterotic stringy black hole mechanics at zeroth order in alpha prime, arXiv:2012.13323 [INSPIRE].
A. Sen, Entropy function for heterotic black holes, JHEP 03 (2006) 008 [hep-th/0508042] [INSPIRE].
G. Guralnik, A. Iorio, R. Jackiw and S.Y. Pi, Dimensionally reduced gravitational Chern-Simons term and its kink, Annals Phys. 308 (2003) 222 [hep-th/0305117] [INSPIRE].
I. Satake, The gauss-bonnet theorem for v-manifolds., J. Math. Soc. Jap. 9 (1957) 464.
A. Sen, Dynamics of multiple Kaluza-Klein monopoles in M and string theory, Adv. Theor. Math. Phys. 1 (1998) 115 [hep-th/9707042] [INSPIRE].
M.F. Atiyah and N. Hitchin, The Geometry and Dynamics of Magnetic Monopoles, Princeton University Press (1988) [INSPIRE].
A. Dabholkar, J.P. Gauntlett, J.A. Harvey and D. Waldram, Strings as solitons and black holes as strings, Nucl. Phys. B 474 (1996) 85 [hep-th/9511053] [INSPIRE].
C.G. Callan, J.M. Maldacena and A.W. Peet, Extremal black holes as fundamental strings, Nucl. Phys. B 475 (1996) 645 [hep-th/9510134] [INSPIRE].
D. Garfinkle, Black string traveling waves, Phys. Rev. D 46 (1992) 4286 [gr-qc/9209002] [INSPIRE].
O. Lunin and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [INSPIRE].
G. Papadopoulos, New half supersymmetric solutions of the heterotic string, Class. Quant. Grav. 26 (2009) 135001 [arXiv:0809.1156] [INSPIRE].
V. Balasubramanian, P. Kraus and M. Shigemori, Massless black holes and black rings as effective geometries of the D1-D5 system, Class. Quant. Grav. 22 (2005) 4803 [hep-th/0508110] [INSPIRE].
R. Emparan and H.S. Reall, A Rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].
R. Emparan and H.S. Reall, Black Rings, Class. Quant. Grav. 23 (2006) R169 [hep-th/0608012] [INSPIRE].
U. Gran, P. Lohrmann and G. Papadopoulos, The Spinorial geometry of supersymmetric heterotic string backgrounds, JHEP 02 (2006) 063 [hep-th/0510176] [INSPIRE].
A. Fontanella and T. Ortín, On the supersymmetric solutions of the Heterotic Superstring effective action, JHEP 06 (2020) 106 [arXiv:1910.08496] [INSPIRE].
U. Gran, G. Papadopoulos and D. Roest, Supersymmetric heterotic string backgrounds, Phys. Lett. B 656 (2007) 119 [arXiv:0706.4407] [INSPIRE].
S. Fubini and H. Nicolai, The Octonionic Instanton, Phys. Lett. B 155 (1985) 369 [INSPIRE].
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. 376 (1996) 329] [hep-th/9502009] [INSPIRE].
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Cano, P.A., Murcia, Á., Ramírez, P.F. et al. On small black holes, KK monopoles and solitonic 5-branes. J. High Energ. Phys. 2021, 272 (2021). https://doi.org/10.1007/JHEP05(2021)272
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DOI: https://doi.org/10.1007/JHEP05(2021)272