# Non-Abelian black holes in string theory

## TL;DR

This paper investigates 5D non-Abelian black holes in string theory, revealing that non-Abelian fields correspond to dissolved D5-branes and do not affect entropy but do contribute to mass, resolving the non-Abelian hair puzzle.

## Contribution

It demonstrates that non-Abelian fields in these black holes are linked to dissolved D5-branes and clarifies their role in entropy and mass, providing a microscopic understanding.

## Key findings

- Non-Abelian fields do not contribute to black hole entropy.
- Dissolved D5-branes account for non-Abelian gauge fields.
- The solution remains valid with alpha prime corrections.

## 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 number16 pages 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 alpha prime corrections are taken into account.