Higher Spin Gravity: Quantization and Algebraic Structures
arXiv:2008.12582
Abstract
The aim of this thesis is to explore the quantum aspects of Higher Spin Gravities (HSGRAs) and their underlining algebraic structures. We give a concise review of HSGRAs followed by three chapters with original results. The first chapter is dedicated to the study of the vacuum one-loop correction of holographic HSGRAs in Anti-de Sitter space. We show that there is a remarkable agreement between the -energy of HSGRAs in the bulk and the predictions coming from the dual CFTs in integer dimensions. We extend this result to continuous dimension and show that vacuum one-loop corrections in HSGRA reproduce the -energy of the Wilson-Fisher CFT in dimension. The second part of the thesis explores the quantum properties of Chiral Higher Spin Gravity - a closed subsector of any other HSGRA in four dimensions. We show that Chiral Theory is UV-finite at one-loop. Moreover, there is an interesting relation between one-loop amplitudes in Chiral HSGRA and the self-dual subsector of QCD. The last part of the thesis is devoted to algebraic structures of HSGRAs. As an application, we construct a formal bosonic HSGRA in in two different ways: by deforming the Joseph relations and by deforming the quasi-conformal realization.
Ph.D. thesis, 268 pages, many figures. Advisor: Prof. Dr. Ivo Sachs