Non-Abelian Black Holes in String Theory

This thesis is devoted to the study of the interaction of non-Abelian Yang-Mills fields with the gravitational field in the context of String Theory and its low energy effective supergravity description. While this type of interactions has been considered for decades within several theoretical frameworks, limited progress has been made, especially when compared to the knowledge we have of the interaction of Abelian fields and gravity. The main reason for that is the complexity of this sort of systems; the differential equations that govern the dynamics of both, gravitational and non-Abelian Yang-Mills fields, are highly non-linear and their resolution represents a formidable problem.

The complexity of these systems, however, can be reduced through the restriction to supersymmetric solutions. This type of solutions, which include extremal black holes, have very special properties. 

Nevertheless, a great deal of information can be acquired from them. 

In particular, not only we can learn about the properties of the classical interaction between the corresponding fields and gravity, but it is also possible to glimpse the quantum nature of certain gravitational systems. The “three-charge” Abelian black hole constitutes the most popular example. This system of String Theory can be understood both as a supersymmetric solution of N = 1 five dimensional supergravity and as a quantum ensamble in which gravity plays no role. One of the greatest achievements of this theory is precisely the computation of the entropy of this black hole from these two perspectives with identical result.

The main result of this thesis is the construction of “three-charge” non-Abelian black holes in supergravity and its interpretation in String Theory. In its turn, this allows for the microscopic computation of its entropy, which at the same time implies the resolution of the non-Abelian hair puzzle in this type of black holes. 

Another prominent result of this thesis is the development of a solution generating technique that allows for the construction of many other families of non-Abelian gravitating solutions in supergravity. 

Their interpretation in terms of fundamental objects of String Theory has only just started.