Abstract
We find the first smooth microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of $\mathcal{N}=1$, $d=5$ Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.
Highlights
This conjecture opened a whole program in the quest to construct smooth microstate geometries in theories of supergravity
The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of N = 1, d = 5 Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon
Even though general microstate geometries lack of this identification, they are still very useful in providing valuable information about the physics of black holes in string theory, see for instance [17,18,19,20,21]
Summary
Smooth microstate geometries are defined as horizonless, regular field configurations without any brane sources but with the asymptotic charges of a black hole. At a technical level this statement implies several conditions that we shall address in the following subsections, being perhaps the most important of those the requirement of working with manifolds with non-trivial topology.. At a technical level this statement implies several conditions that we shall address in the following subsections, being perhaps the most important of those the requirement of working with manifolds with non-trivial topology.5 This fact can be roughly understood from the fact that the existence of non-trivial cycles allows for the presence of measurable asymptotic charges without the introduction of localized brane sources. See for instance [11] for a detailed discussion about this topic. Let us start with a brief description of these manifolds
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