Exploring String Theory Solutions: Black hole thermodynamics with ${\alpha }^{\mathrm{\prime }}$ corrections and type II compactifications

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 ${\alpha }^{\mathrm{\prime }}$ corrections to well-known black hole solutions. We present explicit, analytical expressions for the ${\alpha }^{\mathrm{\prime }}$ 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.