Solving CFTs with weakly broken higher spin symmetry
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In this article, the spectrum of broken currents, for any value of the spin, follows from crossing symmetry, and the spectrum follows from symmetry at first order in the coupling constant, to all values of spin.Abstract:
The method of large spin perturbation theory allows to analyse conformal field theories (CFT) by turning the crossing equations into an algebraic problem. We apply this method to a generic CFT with weakly broken higher spin (HS) symmetry, to the first non-trivial order in the breaking parameter. We show that the spectrum of broken currents, for any value of the spin, follows from crossing symmetry. After discussing a generic model of a single scalar field, we focus on vector models with O(N ) global symmetry. We rediscover the spectrum of several models, including the O(N ) Wilson-Fisher model around four dimensions, the large O(N ) model in 2 < d < 4 and cubic models around six dimensions, not necessarily unitary. We also discuss models where the fundamental field is not part of the spectrum. Examples of this are weakly coupled gauge theories and our method gives an on-shell gauge invariant way to study them. At first order in the coupling constant we show that again the spectrum follows from crossing symmetry, to all values of the spin. Our method provides an alternative to usual perturbation theory without any reference to a Lagrangian.read more
Citations
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References
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Journal ArticleDOI
The Renormalization group and the epsilon expansion
TL;DR: In this paper, the modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory, and the expansion in ϵ = 4−d is explained [ d is the dimension of space (statistical mechanics) or space-time (quantum field theory)].
Journal ArticleDOI
Bounding scalar operator dimensions in 4D CFT
TL;DR: In this article, a theory-independent inequality [phi(2)] 1 was derived for 4D conformal fixed points, where f(d) = 2 + O(root d - 1), which shows that the free theory limit is approached continuously.
Journal ArticleDOI
Holography from Conformal Field Theory
TL;DR: In this paper, it was shown that any CFT with a large-N expansion and a large gap has a local bulk dual, and that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N-2.
Journal ArticleDOI
Conformal four point functions and the operator product expansion
F.A. Dolan,Hugh Osborn +1 more
TL;DR: In this paper, a recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function for scalar fields in conformally invariant theories is derived.
Journal ArticleDOI
The analytic bootstrap and AdS superhorizon locality
TL;DR: In this article, it was shown that every CFT with a scalar operator ϕ must contain infinite sequences of operators with twist approaching τ → 2Δ + 2n for each integer n as l → ∞.