Black holes in string theory with higher-derivative corrections
Author
Ruipérez Vicente, AlejandroEntity
UAM. Departamento de Física Teórica; Instituto de Física Teórica (IFT)Date
2020-09-23Subjects
Cuerdas, teoría de las; Agujeros negros (Astronomía); FísicaNote
Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 23-09-2020Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
The low-energy limit of superstring theories admits a description in terms of an effective eld
theory for its massless modes. The corresponding action is given by a double perturbative
expansion in gs, the string coupling, and in 0, the square of the string length. The leading
term of this expansion is given by one of the different ten-dimensional supergravity theories,
whereas subleading terms involve terms of higher order in derivatives. The work presented in
this thesis is the result of a research program that starts with the study of supersymmetric
solutions of gauged supergravity and reaches the summit with the understanding of the effects
produced by the 0 corrections to solutions of the heterotic superstring e ective action.
This thesis is divided in two parts. The rst one focuses on the supersymmetric solutions
of a minimal extension of the STU model of N = 1; d = 5 supergravity whose main interest
lies on the fact that it can be obtained as a toroidal compacti cation of ten-dimensional N = 1
supergravity coupled to a triplet of SU(2) gauge elds. Concretely, we construct and study
solutions describing black holes and smooth horizonless geometries with non-trivial Yang-Mills
elds.
The understanding of this type of solutions from the framework of string theory serves as
a motivation for the work of the second part of the thesis, which is devoted to the study of
solutions of the effective action of the heterotic string at rst order in 0. The latter does
not simply coincide with the action of N = 1; d = 10 supergravity coupled to a Yang-Mills
vector multiplet as the Green-Schwarz anomaly cancellation mechanism and supersymmetry
enforce us to introduce additional terms in the action. These terms are constructed out of the
spin connection with torsion given by the eld strength associated to the Kalb-Ramond 2-form
and their contributions to the equations of motion are analogous to those of the Yang-Mills
elds. This fact is exploited to construct analytic supersymmetric black-hole solutions with 0
corrections.
The most important lesson to extract from our results is that the mass and the conserved
charges of the black holes do get modi ed by the 0 corrections. This is what one would expect
on physical grounds as the corrections act in the string equations of motion as effective sources
of energy, momentum and charge. This information is crucial to establish a correspondence
between the parameters that characterize the effective or coarse-grained description (the black
hole) and those that characterize the microscopic system of string theory that it describes.
The effects on the charges introduced by the higher-derivative corrections has a major impact
in the understanding of the so-called small black holes, which are an effective description of
a fundamental string with winding and momentum charges. Small black holes are singular
solutions with vanishing horizon area in the supergravity approximation. It has long been
believed that higher-derivative corrections would be able to stretch the horizon, making the
solution regular. Our results reveal that this is not the case at rst order in 0, and that
previous regularizations of heterotic small black holes actually describe a different microscopic
system which is already regular in the supergravity approximation.
The last chapter of the thesis contains the computation of the most general correction to the
four-dimensional Kerr solution when the Einstein-Hilbert term is supplemented with higher
curvature terms up to cubic order, including the possibility of having dynamical couplings.
This general set-up includes, as a particular case, the corrections predicted by the heterotic
superstring effective action
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