Research Projects

The project aims to develop practical calculational tools to study quantum corrections in a perturbative gravity theory in AdS spacetimes. The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence provides an unexpected duality between certain quantum gravity theories in asymptotically AdS spacetimes and certain CFTs living on the asymptotic boundary of AdS in one spacetime dimension less. The objective is to develop efficient methods, both analytical and numerical, to calculate loop amplitudes in the AdS/CFT correspondence, enabling the systematic study of quantum corrections in gravity. The second part of the project will consider discretizations of spacetime, particularly tensor network discretizations of gravity in AdS space. These models have provided profound insights into the emergence of gravitational spacetime as encoding the entanglement structure of the dual CFT, leading to surprising connections between quantum gravity, quantum error-correction, and quantum information theory. However, these models have been limited to two-dimensional AdS space. It is important to test and extend these ideas beyond that, using mathematical structures needed to describe higher-dimensional discretizations and spaces other than AdS. The project plans to study tensor network models of AdS/CFT where the spacetime is replaced by a higher dimensional fractal geometry. The objective is to establish the dynamics of matter fields on such spacetimes and study correlation functions and entanglement properties using analytical methods and numerical techniques. Initial work has pointed to the framework of hyperbolic buildings and Gromov hyperbolicity as the right language to describe holography in this case.