Fundamental Implications of Fields, Strings and Gravity

In the 20th century, General Relativity and Quantum Field Theory emerged as extraordinarily successful theories used to describe physics on very large, and very small scales respectively. They are however incompatible when considering very massive, but very small objects, such as black hole singularities, and the beginning of the universe. New physics is required to provide a unified theory, and String Theory is the most promising candidate, as it can be used to obtain Einstein's equations from a quantum system. It has produced new ways to understand aspects of black hole evaporation, predicted by Hawking, as well as novel "holographic" techniques leading to remarkable relationships between quantities computed using geometric methods and observables in strongly coupled quantum field theories which have hitherto been difficult to calculate. Our proposal is focused on developing new geometric and algebraic techniques to investigate key aspects of quantum theories and geometric solutions related to String Theory.

In holography, we will investigate how geometry emerges from matrix quantum mechanics, and use this to probe how physical properties of black holes vary during the evaporation process, and also to describe how the related quantum states correspond to geometric solutions. Our group has expertise in machine learning and numerical simulation techniques which will be utilized in this analysis. We will also use our expertise in integrability to examine in detail the holographic duality between quantum states and geometric solutions. Integrability provides powerful tools for solving certain quantum systems by extending the solutions away from a limited range of physical parameters, to more general cases. We will develop new methods for analysing massless quantum states in String Theory, leading to a much more complete understanding of these theories. Further progress will also be made in applying "higher geometry" methods to investigate hidden geometric structures...