Understand
This Thesis reviews Vasiliev's approach to Higher-Spin Gauge Theory and contains some original results concerning new exact solutions of the Vasiliev equations and the representation theory of the higher-spin algebra.
- The review part covers the various formulations of the free theory as well as Vasiliev's full nonlinear equations, in particular focusing on their algebraic structure and on their properties in various space-time signatures.
- Then, the original results are presented.
- First, the 4D Vasiliev equations are formulated in space-times with signatures (4-p,p) and non-vanishing cosmological constant, and some new exact solutions are found, depending on continuous and discrete parameters: (a) an SO(4-p,p)-invariant family of solutions; (b) non-maximally symmetric solutions with vanishing Weyl tensors and higher-spin gauge fields, that differ from the maximally symmetric background solutions in the auxiliary field sector; and (c) solutions of the chiral models with an infinite tower of Weyl tensors proportional to totally symmetric products of two principal spinors.