Abstract
We present an asymptotically flat, spherically symmetric, static, globally regular and horizonless solution of SU(2)-gauged \( \mathcal{N}=1 \) , d = 5 supergravity. The SU(2) gauge field is that of the BPST instanton. We argue that this solution, analogous to the global monopoles found in d = 4 \( \mathcal{N}=2 \) and \( \mathcal{N}=4 \) gauged supergravities, describes the field of a single string-theory object which does not contribute to the entropy of black holes when we add it to them and show that it is, indeed, the dimensional reduction on T5 of the gauge 5-brane. We investigate how the energy of the solution is concentrated as a function of the instanton’s scale showing that it never violates the hoop conjecture although the curvature grows unboundedly in the zero scale limit.
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References
M.J. Duff, R.R. Khuri and J.X. Lu, String solitons, Phys. Rept. 259 (1995) 213 [hep-th/9412184] [INSPIRE].
K.S. Stelle, BPS branes in supergravity, in High energy physics and cosmology, Trieste Italy, (1997), pg. 29 [hep-th/9803116] [INSPIRE].
T. Ortín, Gravity and strings, 2nd edition, Cambridge University Press, Cambridge U.K., (2015) [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].
I. Bena and N.P. Warner, Resolving the structure of black holes: philosophizing with a hammer, arXiv:1311.4538 [INSPIRE].
S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
I. Bena, M. Shigemori and N.P. Warner, Black-hole entropy from supergravity superstrata states, JHEP 10 (2014) 140 [arXiv:1406.4506] [INSPIRE].
I. Bena et al., Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett. 117 (2016) 201601 [arXiv:1607.03908] [INSPIRE].
M.S. Volkov and D.V. Gal’tsov, Gravitating non-Abelian solitons and black holes with Yang-Mills fields, Phys. Rept. 319 (1999) 1 [hep-th/9810070] [INSPIRE].
D.V. Gal’tsov, Gravitating lumps, in Proceedings of the 16th International Conference on General Relativity and Gravitation (GR16), N.T. Bishop and S.D. Maharaj eds., World Scientific, Singapore, (2002) [hep-th/0112038] [INSPIRE].
E. Winstanley, Classical Yang-Mills black hole hair in anti-de Sitter space, Lect. Notes Phys. 769 (2009) 49 [arXiv:0801.0527] [INSPIRE].
M.S. Volkov, Hairy black holes in the XX-th and XXI-st centuries, arXiv:1601.08230 [INSPIRE].
M. Hübscher, P. Meessen, T. Ortín and S. Vaulà, N = 2 Einstein-Yang-Mills’s BPS solutions, JHEP 09 (2008) 099 [arXiv:0806.1477] [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].
J. Bellorín, Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings, Class. Quant. Grav. 26 (2009) 195012 [arXiv:0810.0527] [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].
P. Meessen, Supersymmetric coloured/hairy black holes, Phys. Lett. B 665 (2008) 388 [arXiv:0803.0684] [INSPIRE].
P. Bueno, P. Meessen, T. Ortín and P.F. Ramírez, N = 2 Einstein-Yang-Mills’ static two-center solutions, JHEP 12 (2014) 093 [arXiv:1410.4160] [INSPIRE].
P. Meessen and T. Ortín, N = 2 super-EYM coloured black holes from defective Lax matrices, JHEP 04 (2015) 100 [arXiv:1501.02078] [INSPIRE].
T. Ortín and P.F. Ramírez, A non-Abelian black ring, Phys. Lett. B 760 (2016) 475 [arXiv:1605.00005] [INSPIRE].
P.F. Ramírez, Non-Abelian bubbles in microstate geometries, JHEP 11 (2016) 152 [arXiv:1608.01330] [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, Black holes in string theory, Ph.D. thesis, Princeton University, Princeton U.S.A., (1996) [hep-th/9607235] [INSPIRE].
P.A. Cano, P. Meessen, T. Ortín and P.F. Ramírez, Non-Abelian black holes in string theory, arXiv:1704.01134 [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.A. Harvey and J. Liu, Magnetic monopoles in N = 4 supersymmetric low-energy superstring theory, Phys. Lett. B 268 (1991) 40 [INSPIRE].
A.H. Chamseddine and M.S. Volkov, Non-Abelian BPS monopoles in N = 4 gauged supergravity, Phys. Rev. Lett. 79 (1997) 3343 [hep-th/9707176] [INSPIRE].
A.H. Chamseddine and M.S. Volkov, Non-Abelian solitons in N = 4 gauged supergravity and leading order string theory, Phys. Rev. D 57 (1998) 6242 [hep-th/9711181] [INSPIRE].
A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167 [Erratum ibid. B 353 (1991) 565] [INSPIRE].
A.P. Protogenov, Exact classical solutions of Yang-Mills sourceless equations, Phys. Lett. B 67 (1977) 62 [INSPIRE].
P.B. Kronheimer, Monopoles and Taub-NUT spaces, M.Sc. dissertation, Oxford University, Oxford U.K., (1995).
M.J. Duff, R.R. Khuri and J.X. Lu, String and five-brane solitons: singular or nonsingular?, Nucl. Phys. B 377 (1992) 281 [hep-th/9112023] [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, Worldbrane actions for string solitons, Nucl. Phys. B 367 (1991) 60 [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, S. Cucu, T. de Wit, J. Gheerardyn, S. Vandoren and A. Van Proeyen, N = 2 supergravity in five-dimensions revisited, Class. Quant. Grav. 21 (2004) 3015 [Corrigendum ibid. 23 (2006) 7149] [hep-th/0403045] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K., (2012) [INSPIRE].
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].
P.A. Cano, T. Ortín and C. Santoli, Non-Abelian black string solutions of N = (2, 0), D = 6 supergravity, JHEP 12 (2016) 112 [arXiv:1607.02595] [INSPIRE].
M. Hübscher, 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].
E.B. Bogomolny, Stability of classical solutions, Sov. J. Nucl. Phys. 24 (1976) 449 [Yad. Fiz. 24 (1976) 861] [INSPIRE].
G. Etesi and T. Hausel, New Yang-Mills instantons on multicentered gravitational instantons, Commun. Math. Phys. 235 (2003) 275 [hep-th/0207196] [INSPIRE].
P. Meessen, T. Ortín and P.F. Ramírez, Multicenter non-Abelian black hole solutions of N = 2, d = 4 supergravity,inpreparation.
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].
B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, JHEP 11 (2011) 127 [hep-th/0304094] [INSPIRE].
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Cano, P.A., Ortín, T. & Ramírez, P.F. A gravitating Yang-Mills instanton. J. High Energ. Phys. 2017, 11 (2017). https://doi.org/10.1007/JHEP07(2017)011
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DOI: https://doi.org/10.1007/JHEP07(2017)011