Exact results in quantum deformed holography
Integrable models --- of which the Kepler problem or the Heisenberg spin-chain are celebrated examples --- are the exactly solvable building blocks upon which the whole theoretical physics monument stands. While they describe a simplified version of nature, their tractable structure gives invaluable insight into complicated systems closer to the real world. Remarkably, they also lead to major advances in our understanding of quantum gravity and holography, an area in which the need for analytical tools is critical due to the lack of experiments. Integrable theories appear in instances of the AdS/CFT correspondence, a duality relating string theories on Anti-de-Sitter space-times to Conformal Field Theories living on the boundary of these space-times. The aim of this project is to explore extended versions of AdS/CFT holography through the study of integrable quantum deformations. The specific objectives are (O.1) to establish new connections between quantum deformations of superstrings, (O.2) to compute physical observables in these theories via adapted integrability techniques, (O.3) to explore the quantum properties of these deformations and (O.4) to constrain their dual theories. Constructing and studying new deformations of AdS/CFT has the potential to dramatically expand the scope of our understanding of string theory, quantum field theories at finite coupling and holography. Integrability is expected to provide a crucial guiding principle and invaluable tool in harnessing such a potential. Moreover, this project will connect mathematical and physical aspects of quantum group.