# Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect

## TL;DR

This paper constructs a five-dimensional Einstein-Yang-Mills black hole with a Meron field, revealing a spin-from-isospin effect that induces fermionic behavior from a purely bosonic setup, with implications for AdS/CFT correspondence.

## Contribution

It presents an analytic 5D black hole solution with a Meron gauge field, demonstrating a novel spin-from-isospin effect and analyzing its thermodynamics and holographic implications.

## Key findings

- Black hole solution with finite mass and phase transition.
- Evidence of fermionic behavior emerging from bosonic fields.
- Implications for AdS/CFT correspondence in the asymptotic case.

## Abstract

We construct an analytic black hole solution in $SU(2)$ Einstein-Yang-Mills theory in five dimensions supporting a Meron field. The gauge field is proportional to a pure gauge and has a non-trivial topological charge. The would-be singularity at the Meron core gets shielded from the exterior by the black hole horizon. The metric has only one integration constant, namely, its ADM mass, which is shown to be finite once an appropriate boundary term is added to the action. The thermodynamics is also worked out, and a first-order phase transition, similar to the one occurring in the Reissner-Nordstr{\"o}m case is identified. We also show that the solution produces a \mbox{\textit{spin from isospin effect}}, i.e., even though the theory is constructed out of bosons only, the combined system of a scalar field and this background may become fermionic. More specifically, we study scalar excitations in this purely bosonic background and find that the system describes fermionic degrees of freedom at spatial infinity. Finally, for the asymptotically $AdS_{5}$ case, we study its consequences in the context of the AdS/CFT correspondence.