On Low-Dimensional Black Holes in String Theory

Abstract

It has been a long-standing goal of theoretical physics to obtain a fully quantum description of black holes with an explicit understanding of its microstates and its eventual evaporation. In this thesis, we develop new tools as a step toward constructing the microstates and subsequent Lorentzian evolution of a two-dimensional string theory background known as the cigar black hole. Specifically, we introduce the technique of angular quantization in 2d CFT, wherein one foliates the sphere by constant-angle rays ending on two local operators and evolves angularly around them via a Rindler Hamiltonian. We describe in detail how this formalism naturally defines CFTs in Minkowski space with specified asymptotic charges. In the context of string theory, angular quantization is needed to provide a Lorentzian interpretation of worldsheet diagrams which involve operator insertions having nontrivial winding around target space Euclidean time. Applying our results to this case, we obtain a general picture of a new type of string which is neither open nor closed that we instead dub "stretched". As a special case of stretched strings, we find heuristic agreement with Maldacena's "long strings" in the c=1 string theory. Finally, in another example where Euclidean time-winding operators are involved, we construct small black holes, or "string stars", in three-dimensional AdS space via a worldsheet analysis underlying the Horowitz-Polchinski methodology. As a result, we obtain explicit string star backgrounds near the Hagedorn temperature, whose Lorentzian target space description again involves an ensemble of stretched strings.