Exploring String Theory Solutions: Black hole thermodynamics with $\alpha'$ corrections and type II compactifications

Abstract

This PhD thesis explores the properties of certain solutions in stringy effective field theories (EFTs). In the context of heterotic string theory (HST), we study $\alpha'$ corrections to well-known black hole solutions. We present explicit, analytical expressions for the $\alpha'$ corrections to these solutions and fully characterize their thermodynamics refining Iyer-Wald's prescription. In the context of type II theories, we study compactifications of the form $X_4 \times X_6$. We begin with AdS$_4$ Calabi-Yau orientifold compactifications with localized sources and investigate their non-perturbative stability. We then consider internal manifolds with non-trivial integer (co)homology and demonstrate how integer homology data can leak into the EFT.