On Quantum Corrections in String Compactifications: Effective Actions and Black Holes

The overarching theme of this thesis is the study of quantum effects in string theory, a theory of quantum gravity.

In the first part of this thesis we focus on compactifications of type II string theory and M-theory on Calabi-Yau three- and fourfolds. In all cases we take leading higher derivative corrections into account. For the case of compactifications on Calabi-Yau threefolds we obtain four- and five dimensional effective actions. The higher-derivative corrections lead to corrections in the low-energy effective actions and we compute the couplings which govern these corrections explicitly. Furthermore, we investigate compactifications of M-theory with higher derivatives on Calabi-Yau fourfolds with a single Kähler modulus. In this setting we are able to identify a new correction to the three-dimensional N=2 two-derivative effective action.

The second part of this thesis studies embeddings of black holes in type IIB/F-theory utilizing D3-branes. These black holes descend from strings in compactifications type IIB/F-theory to six dimensions. On the worldvolume of these strings there is a two-dimensional superconformal field theory (SCFT) with N = (0,4) supersymmetry, which we investigate both from a microscopic and macroscopic point of view. We compute anomaly coefficients of these SCFTs and find that for the macroscopic computations the inclusion of one loop corrections play a very important role to obtain the expected results. These anomaly coefficients may then be used to compute the entropy of the associated black hole.