# Higher-spin fields In flat space ($D\ge4$), there are no-go theorems that rule out interacting QFTs with massless higher-spin fields. This can be circumvented in a few ways, e.g., by adding a cosmological constant. But even so, higher-spin fields are surprisingly constrained. In AdS$_{D>3}$, (finitely many) higher-spin fields violate causality. Massless higher-spin fields, which are dual to conserved higher-spin currents in CFT, are also disallowed for symmetry reasons. ## Refs - review - [[2010#Bekaert, Boulanger, Sundell (Review)]]: non-technical - Fierz-Pauli Lagrangian for massive higher-spin fields - Hagen and Singh - Fronsdal theory for massless higher-spin fields - [[1978#Fronsdal]] - gauge-invariant formulations - [[2023#Fegebank, Kuzenko]]: quantisation - [[2024#Fegebank, Kuzenko]]: equivalence between a traceful and a traceless formulation - 3d theories - [[2024#Sharapov, Skvortsov, Sukhanov]]