Higher Spin Gravity: Quantization and Algebraic Structures

TL;DR

This thesis investigates the quantum properties and algebraic structures of Higher Spin Gravities, demonstrating their agreement with dual CFT predictions, UV finiteness in chiral sectors, and constructing new algebraic models in AdS spaces.

Contribution

It provides original results on one-loop corrections, UV finiteness of Chiral HSGRA, and new algebraic constructions of HSGRA in AdS spaces.

Findings

Vacuum one-loop corrections match dual CFT predictions.

Chiral HSGRA is UV-finite at one-loop.

Constructed a formal bosonic HSGRA in AdS_5.

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 $F$-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 $F$-energy of the Wilson-Fisher CFT in $4-\epsilon$ 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 $AdS_5$ in two different ways: by deforming the Joseph relations and by deforming the quasi-conformal realization.