# Higher-spin operators in CFT ## Higher-spin conserved currents It was shown in [[2015# by Hartman, Jain, and Kundu]] that a CFT cannot have a finite number of higher-spin conserved currents. Their method was to study the [[0619 Lightcone OPE|Lorentzian OPE]] and show that the dominant operator exchange near the lightcone must have spin $\le 2$. ## Single-trace higher-spin operators A [[0122 Holographic CFT|holographic CFT]] should have a large gap to higher-spin single-trace operators. ## Refs - proof of no (finitely many) higher-spin conserved currents in CFT - [[2011#Maldacena, Zhiboedov]]: 3d - [[2013#Boulanger, Ponomarev, Skvortsov, Taronna]]: higher than 3d; using higher-spin algebras - [[2015#Alba, Diab]]: higher than 3d - [[2015#Hartman, Jain, Kundu]]: any dimension - $\mathcal{W}_N$ symmetry - [[2017#Afkhami-Jeddi, Colville, Hartman, Maloney, Perlmutter]]: a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the [[0033 Central charge|central charge]] - using chaos bound - [[2016#Perlmutter]] ## Related - [[0122 Holographic CFT]]