Constraining conformal field theories with a higher spin symmetry

2013/05/14 by Juan Maldacena, Alexander Zhiboedov · 3 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Chromodynamics and Particle Interactions #Conserved current #Conformal field theory #Physics #Conserved quantity #Spin (aerodynamics) #Boson #Theoretical physics #Fermion #Symmetry (geometry) #Current (fluid) #Field (mathematics) #Tensor (intrinsic definition) #Homogeneous space #Field theory (psychology) #Mathematical physics #Quantum mechanics #Conformal map #Mathematics #Noether's theorem #Geometry #Pure mathematics

paper · doi:10.1088/1751-8113/46/21/214011

openalex publication_date 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We study the constraints imposed by the existence of a single higher spin conserved current on a three-dimensional conformal field theory (CFT). A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of N free bosons or free fermions. This is an extension of the Coleman–Mandula theorem to CFT’s, which do not have a conventional S-matrix. We also briefly discuss the case where the higher spin symmetries are ‘slightly’ broken.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

Citations

• Massless higher spins and holography
• All possible generators of supersymmetries of the S-matrix
• THE MODELS OF TWO-DIMENSIONAL CONFORMAL QUANTUM FIELD THEORY WITH Zn SYMMETRY
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Cited by

• Refined stable pair invariants for E-, M- and [p, q]-strings
• A proof of the conformal collider bounds
• Mixed-symmetry tensor conserved currents and AdS/CFT correspondence
• Conformal symmetry [wikipedia]

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