Stringy geometry: quantum corrections and the fate of string compactifications from spacetime and the worldsheet
This project uses newly developed geometric structures to understand quantum corrections in string theory from both a worldsheet and spacetime perspective.

The major goal is to prove that supergravity solutions with flux can be quantum corrected to give consistent string compactifications. I will also investigate whether these new geometric structures can shed light on strongly coupled heterotic worldsheet models. I will do this by combining my experience with the mathematics that underlies flux compactifications with insights from supergravity and worldsheet methods. This will greatly expand my knowledge in both physics and mathematics and bring me into close working relationships with researchers at the University of Chicago and Sorbonne Universite.

The key difference between my approach and existing work is the use of newly developed techniques in differential geometry that provide a unified framework for analysing flux compactifications - in particular, generalisations of G-structures within generalised geometry.

The proposed research tackles a fundamental problem: we do not know whether the many supergravity solutions used in phenomenology or AdS/CFT define honest string theory solutions. One output of this project will be a natural language for stringy corrections - this has applications in formal aspects of string theory and phenomenology, including moduli stabilisation, finding new non-Kahler heterotic solutions and the existence of de Sitter vacua. Progress on any one of these would be an valuable contribution to the most important problems in the field, ensuring the ongoing international competitiveness of theoretical physics in the EU.

The proposed research is interdisciplinary due to considerable overlap with differential geometry and conformal field theory. The proposal includes plans for transfer of knowledge between the applicant and the host institutions, acquisition of new knowledge areas, professional development and outreach.