Abstract
We study a family of 5-dimensional non-Abelian black holes that can be obtained by adding an instanton field to the well-known D1D5W Abelian black holes. Naively, the non-Abelian fields seem to contribute to the black-hole entropy but not to the mass due to their rapid fall-off at spatial infinity. By uplifting the 5-dimensional supergravity solution to 10-dimensional Heterotic Supergravity first and then dualizing it into a Type-I Supergravity solution, we show that the non-Abelian fields are associated to D5-branes dissolved into the D9-branes (dual to the Heterotic "gauge 5-branes") and that their associated RR charge does not, in fact, contribute to the entropy, which only depends on the number of D-strings and D5 branes and the momentum along the D-strings, as in the Abelian case. These "dissolved" or "gauge" D5-branes do contribute to the mass in the expected form. The correct interpretation of the 5-dimensional charges in terms of the string-theory objects solves the non-Abelian hair puzzle, allowing for the microscopic accounting of the entropy. We discuss the validity of the solution when α′ corrections are taken into account.
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Cano, P.A., Meessen, P., Ortín, T. et al. Non-Abelian black holes in string theory. J. High Energ. Phys. 2017, 92 (2017). https://doi.org/10.1007/JHEP12(2017)092
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DOI: https://doi.org/10.1007/JHEP12(2017)092