AdS/CFT Integrability in New Regimes: Strong Coupling and Low Dimensions

This project will treat quantum field theories and string theories that exhibit integrability and supersymmetry and make progress towards their exact solution.

The most prominent example of such a theory is the four-dimensional maximally supersymmetric Yang-Mills theory and its dual string theory. The most advanced integrability method to study this model is the Quantum Spectral Curve (QSC).

However, when the theory is strongly interacting there is no efficient way to solve the QSC nor do we know in general how to extend the QSC from four dimensions to lower dimensions.We will address these shortcomings by constructing novel methods to treat the QSC equations at strong coupling and generalise the formalism to a family of theories living in a three-dimensional anti-de Sitter space.

These two tasks are not separate but complementary, for example, reliable data describing the three-dimensional theories is only available at strong coupling.

The starting point will be numerical methods and a recent conjecture for a specific low-dimensional QSC.The outcome of this project will be state-of-the-art tools using which we can obtain long-sought-after data and predictions. The results will have applications within strongly coupled quantum field theories and low-dimension holography.

The project will shed light on long-standing questions such as the quantisation of string theory on curved space.