520026 VU Introduction to higher-spin gravity (2023W)

Gauge theories are a successful theoretical framework for physical theories. A simple example is electrodynamics which is invariant when the gradient of an arbitrary function is added to the four-potential. The standard model of particle physics is based on a gauge theory (electroweak interactions, QCD), and also general relativity is formulated as a gauge theory where the gauge symmetry is the invariance under reparametrisations. Whereas electrodynamics and the standard model interactions are referred to as spin-1 gauge theories (the corresponding particles are helicity 1 gauge bosons), gravity can be viewed as a spin-2 gauge theory (the postulated graviton has helicity 2).

Higher-spin gauge theories generalise the framework of gauge theories to interactions that are based on fields of spin higher than 2. Although they do not seem to have a direct phenomenological application, they provide an interesting class of generalised gravity theories, which challenge our view on geometry and causality. They are supposed to be related to a specific limit of string theory, and similar to string theory they show a holographic duality to lower-dimensional field theories.

Higher-spin theories are far from being understood and they are a current topic of research. In the course we will focus on theories in three spacetime-dimensions, where gravity and higher-spin interactions are not propagating and the theories become more tractable. We start by discussing free higher-spin fields in any dimension, and then present a formulation of interacting higher-spin theories in three dimensions. In this context we describe the asymptotic symmetries on asymptotically Anti-de Sitter spacetimes. We then discuss the quantisation of the symmetry algebras in the context of dual quantum field theories. Along the way we will get familiar with various concepts of theoretical physics like constrained Hamiltonian systems or two-dimensional conformal field theories.