Supervisor: Dr Tarek Anous
Project description:The aim of this research project is to understand how to build models of de Sitter space, a maximally symmetric spacetime that describes a universe whose volume grows exponentially in time. Our aim will be to build unitary, interacting quantum mechanics (QM) and quantum field theory (QFT) models whose isometry group is that of d-dimensional de Sitter space SO(1,d). To do so, we will rely first on integrable models for d <3. We will take a two-pronged approach: we will first understand how to suitably modify Calogero-type models for our purposes, these systems are ideal since their isometry group can be associated with simple Lie algebras. Concurrently we will identify matrix models whose eigenvalue dynamics matches these novel Calogero-type models. We will follow up by studying these matrix models in the limit where their rank becomes very large. In standard examples, this gives rise to an emergent target space, and a string expansion, much like in conventional string theory. The expectation is to find a similar structure in the de Sitter case, but with crucial differences since there is no yet understanding of how to put strings in de Sitter. As a third avenue for studying this problem, we will look at statistical field theories with disorder. Recently, I demonstrated that an interacting quantum mechanics with a sphere target space has a conformal fixed point if it is tuned to lie in a spin glass phase. In this project we will determine if this observation holds true in field theory. If so we will have constructed a conformal field theory with a sphere target space, evading a famous no-go theorem, thus opening a potential door for studying interacting strings on de Sitter.
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