Higher-spin symmetry in quantum gravity and conformal field theory

Higher-spin gravity theories are generalizations of Einstein's general relativity that involve towers of interacting massless fields of all spins (including, in particular, the graviton). These theories have an infinite dimensional higher-spin gauge symmetry, and can be consistently constructed in the presence of a non-zero cosmological constant. I will give an overview of higher-spin theories, with a focus on their role in the context of the AdS/CFT correspondence, a remarkable "holographic"
duality between quantum gravity in anti-de Sitter (AdS) space and a conformal field theory (CFT) in one less dimension. In the simplest version of these dualities, higher-spin gravity appears to be holographically dual to free quantum field theories, which enjoy an exact higher-spin symmetry. At the same time, higher-spin gravity also provides dual gravitational descriptions of certain interacting CFTs, such as the Wilson-Fisher fixed point of the O(N) vector model, Gross-Neveu model, and generalizations of these models that involve Chern-Simons gauge theory. These CFTs have weakly broken higher-spin symmetries, and are AdS/CFT dual to higher-spin gravity theories in AdS where the higher-spin symmetry is broken by quantum effects.