Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry
Xavier Bekaert, Nicolas Boulanger, Andrea Campoleoni, Marco Chiodaroli, Dario Francia, Maxim Grigoriev, Ergin Sezgin, Evgeny Skvortsov
TL;DR
HiSGRA advances the idea that extending gravity to massless higher-spin fields with spins $s>2$ and their enlarged gauge symmetry could constrain quantum gravity. The paper surveys results such as vanishing or CFT-free-energy-aligned one-loop corrections and holographic vector-model dualities, while outlining a broad future program spanning quantum gravity, supersymmetry, conformal field theory, black-hole scattering, non-relativistic systems, and deep mathematical foundations. It emphasizes three pillars: building finite/renormalizable theories via cohomological classifications, extending to massive HS spectra, and strengthening HS/CFT holography with rigorous quantization and twistor methods. The authors argue that developing background-independent, mathematically robust HiSGRA frameworks and connecting to string/M-theory could yield predictive, potentially finite models of quantum gravity with rich implications for cosmology and black hole physics.
Abstract
Higher Spin Gravity refers to extensions of gravity including at least one field of spin greater than two. These extensions are expected to provide manageable models of quantum gravity thanks to the infinite-dimensional (higher spin) gauge symmetry constraining them. One of the key aspects of Higher Spin Gravity/Symmetry is the range and diversity of topics it embraces: (a) higher spin fields play a role in quantum gravity, AdS/CFT, string theory and are expected to have important consequences in cosmology and black hole physics; (b) higher spin symmetry finds applications in Conformal Field Theories, condensed matter systems and dualities therein; (c) these models often rely on tools developed in the study of the mathematical foundations of QFT or in pure mathematics: from deformation quantization and non-commutative geometry to conformal geometry, graded geometry (including BV-BRST quantization), and geometry of PDEs. Recent exciting applications also involve (d) modelling the coalescence of black hole binaries as scattering of massive higher spin particles.