Exploring the landscape of string theory flux vacua using exceptional field theory

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String theory, our most-developed theory of quantum gravity, is only consistent in ten dimensions. Nonetheless, we can obtain insight into lower-dimensional physics by "compactifying" it, i.e. considering string theory on spaces where some dimensions make up a compact space. Many properties of the lower-dimensional theories, such as the spectrum of particles, are encoded in the geometry of the compact space. This allows us to obtain string theory predictions for our universe.Moreover, "holography" relates string theory on D-dimensional Anti-de Sitter space, a certain negatively-curved space, times a compact space to quantum field theories without gravity in D-1 dimensions. Over the last 20 years, this has led to tremendous new insight into quantum field theories such as those underlying the strong nuclear force or superconductors.In both string phenomenology and holography, it is important to consider compactifications pierced by "fluxes", higher-dimensional generalisations of electromagnetic flux. Yet, we are lacking a systematic understanding of flux compactifications. As a result, string phenomenology has only been able to study a subset of possible compactifications, where the fluxes weakly "backreact" on the geometry. Moreover, it is difficult to construct deformations of AdS vacua and to study the space of AdS solutions, both of which contain important information about strongly-coupled quantum field theories which can often not be studied directly.The difficulty in studying flux compactifications stems from our reliance on Riemanniangeometry. In this project, I will instead use the recently-formulated Exceptional Field Theory, which I have substantially helped develop. In this formalism, fluxes and gravitational degrees of freedom are unified, providing an entirely natural language in which to study flux compactifications. Moreover, it allows us to study non-geometric string backgrounds, on which our usual notions of spacetime break down and which cannot be analysed using conventions tools. Yet, these non-geometric backgrounds have many desirable phenomenological properties and may provide new examples of holographic dualities.This project will systematically investigate and classify the supersymmetric flux vacua of string theory and their deformations, and analyse their role in realistic string-models of nature and holography. The specific goals are to:[A] Analyse the moduli space and gauge groups of generic 4-dimensional supersymmetric Minkowski vacua.[B] Understand the topology of supersymmetric Minkowski flux vacua and develop new methods of constructing backreacted flux vacua.[C] Classify all supersymmetric AdS vacua of 10-/11-dimensional supergravity, and search for non-geometric AdS vacua of string theory.[D] Construct finite supersymmetric and supersymmetry-breaking deformations of supersymmetric AdS vacua.[E] Develop a holographic dictionary that is useful for precision tests of holography.