Machine Learning Gravity Compactifications on Negatively Curved Manifolds

In theories with extra dimensions, four-dimensional vacua are non-trivial even classically. In fact, even a configuration that looks like a vacuum in four dimensions can have (and often has) a very rich structure for the geometry and the matter fields in the extra dimensions. The study of these structures, which are simultaneously rich and highly constrained by the UV completion of the theory, is important to extract the fourdimensional physics, as well as for holographic approaches to quantum gravity. As we will discuss in detail below, the problem of directly solving the equations of motion for vacuum compactifications is computationally challenging, and a popular approach to bypass this challenge is to exploit supersymmetry in some form. This is the case, for example, of the famous KKLT proposal [1] for obtaining de Sitter vacua, which uses as starting point a supersymmetric Calabi-Yau compactification, on top of which supersymmetry-breaking effects are added. But this is true also for AdS: most of the explicitly known AdS compactifications of string/M-theory are either supersymmetric, obtained by starting from supersymmetric compactifications and turning on supersymmetry breaking effects, or as non-supersymmetric vacua of lower-dimensional supergravities obtained from reduction around supersymmetry vacua.