Conformal field theories with infinitely many conservation laws

Abstract

Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [BNRT]. Recently, conformal field theories "with higher spin symmetry" were considered for D=3 in [MZ] where a similar result was obtained (exploiting earlier study of CFT correlators). We suggest that the proper generalization of the notion of a 2D chiral algebra to arbitrary (even or odd) dimension is precisely a CFT with an infinite series of conserved currents. We shall recast and complement (part of) the argument of Maldacena and Zhiboedov into the framework of our earlier work. We extend to D=4 the auxiliary Weyl-spinor formalism developed in [GPY] for D=3. The free field construction only follows for D>3 under additional assumptions about the operator product algebra. In particular, the problem of whether a rational CFT in 4D Minkowski space is necessarily trivial remains open.

24 pages, Lecture at the TH Journal Club (CERN, February 2012)

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Cited by in corpus (9)

• Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
• Four-point correlation function of stress-energy tensors in N=4 superconformal theories
• Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory
• Constraining conformal field theories with a higher spin symmetry in d=4
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Superfield twist-$2$ operators in $\mathcal{N}=1$ SCFTs and their renormalization-group improved generating functional in $\mathcal{N}=1$ SYM theory
• Studying Quantum Field Theory
• Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins
• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories