Not So Flat Metrics

In order to be in control of the ${\alpha }^{\mathrm{\prime }}$ derivative expansion, geometric string compactifications are understood in the context of a large volume approximation. In this letter, we consider the reduction of these higher derivative terms, and propose an improved estimate on the large volume approximation using numerical Calabi-Yau metrics obtained via machine learning methods. Further to this, we consider the ${\alpha }^{\mathrm{\prime }3}$ corrections to numerical Calabi-Yau metrics in the context of IIB string theory. This correction represents one of several important contributions for realistic string compactifications – alongside, for example, the backreaction of fluxes and local sources – all of which have important consequences for string phenomenology. As a simple application of the corrected metric, we compute the change to the spectrum of the scalar Laplacian.