In this thesis, we study microstate geometries of black holes in string theory and explore several aspects of integrabile Conformal Field Theories (CFTs). The first goal of this thesis is to get insights into physics of black holes by constructing a large new family of regular geometries that would account for the Bekenstein--Hawking entropy. Several classes of such states have been found in the past, but the number of known solutions is not sufficient to fully account for the entropy of macroscopic black holes. In this thesis we construct a large new family of regular microstate geometries and identify a new superposition principle for them. This feature stems from a hidden linear structure of equations governing our geometries, and it makes the dynamical system solvable or integrable. The second goal of this thesis is to explore the space of integrable string theories. Being analytically solvable, such models lead to important insights into the structure of strongly--coupled systems. While there is no algorithmic procedure for finding new integrable theories, in certain cases one can promote isolated examples into continuous families of solvable systems by performing so--called $\eta$-- and $\lambda$--deformations. In this thesis we combine the methods associated with these two deformations to construct multi--parameter families of integrable models and to explore analytical structure of the resulting theories. The third goal of this thesis is to study excitations of integrable backgrounds in string theory. The conventional approach to such analyses is based on separation of variables associated with continuous geometric symmetries, but it breaks down for the deformed models since all such symmetries are lost. Nevertheless, in this thesis we completely determine the spectra of scalar fields on several $\lambda$--deformed backgrounds by combining algebraic and group-theoretic methods.
|Commitee:||Caticha, Ariel, Jain, Vivek, Mann, Nelia, Robbins, Daniel|
|School:||State University of New York at Albany|
|School Location:||United States -- New York|
|Source:||DAI-B 80/03(E), Dissertation Abstracts International|
|Keywords:||Conformal Field Theories, Integrability, String theory|
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