Large spin systematics in CFT

By L. Alday, A. Bissi, Tomasz Lukowski. Journal of High Energy Physics, 2015

209 citations recorded by the source corpus.

Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analyticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new “reciprocity” principle for structure constants. We argue that these results extend also to non-conformal theories.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/55a685fa1952c69f629f8f0c94528979433c7a22

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Citations in the corpus

A Mellin space approach to the conformal bootstrap (2016, background): “d perhaps amenable to analytic treatment. These numerical methods have also been extended to supersymmetric theories [13]. Furthermore, there are also certain analytic results available at large spin [14, 15, 16, 17]. However, the existing approaches do not appear to be well suited for extracting an”
Quantum gravity from conformal field theory (2017, background): “Following [59] in this context, for twist 4 operators, it can be phrased as follows.”
The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, background): “However, [61] argued that the large-spin expansion can be extended to include contributions from operators with h0 > ∆φ.”
Gravitational S-matrix from CFT dispersion relations (2017, background): “ before, the angle brackets represent sums over all nearly-degenerate operators. The reciprocity principle implies that these are the combinations that admit an expansion in integer powers of J2, see [27]. In the relations above weighted averages are shown explicitly. The unknown expansions should b”
Light-ray operators in conformal field theory (2018, methodology): “Caron-Huot’s Lorentzian inversion formula has many other useful applications, for example to large-spin perturbation theory and the lightcone bootstrap [17–26], and to the SYK model [27–30].”
Analyticity in spin in conformal theories (2017, background): “Precisely this formula, and the existence of a function C(z, β), has been deduced empirically before from large-J expansions, see [11, 33].”
On the CFT operator spectrum at large global charge (2015, methodology): “The large-J limit has also simplified the analysis of the high-spin spectrum in CFT [2–5] and the worldsheet theory in the confining regime [6].”
A proof of the conformal collider bounds (2016, background): “Another perspective comes from analytical studies of the bootstrap in the lightcone limit, which reveal a direct relation between couplings of low-twist operators and the asymptotic behavior of CFT spectra at large spin [16, 17], extended further in [18–28].”
An algebraic approach to the analytic bootstrap (2015, methodology): “Following [6], let us start by recalling from [8] the existence of a Casimir operator C such that ∫ ∞”
Loops in AdS from conformal field theory (2016, methodology): “Nevertheless, solutions can be constructed as a systematic expansion around large spin, adapting the machinery of [52–54].”