Convexity and liberation at large spin

By Z. Komargodski, A. Zhiboedov. 2012

546 citations recorded by the source corpus.

A bstractWe consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity property of dimensions of spinning operators of the original CFT. We further investigate the dimensions of spinning operators via the crossing equations in the light-cone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists τ1, τ2 appear in the spectrum, there are operators whose twists are arbitrarily close to τ1 + τ2. We characterize how τ1 + τ2 is approached at large spin by solving the crossing equations analytically. We find the precise form of the leading correction, including the prefactor. We compare with examples where these observables were computed in perturbation theory, or via gauge-gravity duality, and find complete agreement. The crossing equations show that certain operators have a convex spectrum in twist space. We also observe a connection between convexity and the ratio of dimension to charge. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6ff50613212ca70d48f531f43f8d5852c8d4156b

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Citations in the corpus

Large spin systematics in CFT (2015, unknown): “These results include the next order correction to the results of [7, 8], but in addition imply conditions for the higher order terms.”
Defects in conformal field theory (2016, methodology): “Besides specific examples, one more motivation for our work is provided by the recent progress in exploring the space of CFTs using the conformal bootstrap [36, 37, 38, 39, 40, 41, 42].”
An algebraic approach to the analytic bootstrap (2015, methodology): “As explained in [4, 5] the presence of the identity operator in the crossed channel implies the existence of double trace-like higher spin operators, which we denote as [O,O]s, whose twist approaches 2∆ for large spin.”
Bootstrapping the O(N ) vector models (2013, background): “The representation as a sum over poles in ∆ may also be useful for making general analytic arguments (going beyond the large spin arguments of [55, 56]) in the context of the conformal bootstrap.”
Universality of long-distance AdS physics from the CFT bootstrap (2014, background): “It is convenient to state the results [6, 7] in terms of the anomalous dimension γAB(n, `) ≡ ∆AB− (∆A+ ∆B + 2n+ `) and the OPE coefficients cAB(n, `) for the operator [OAOB]n,`.”
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, background): “As was emphasized in its recent discussion in [19], its derivation uses the polynomial boundedness of a certain scattering amplitude, which is still conjectural (although plausible) at present.”
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, 3] and the worldsheet theory in the confining regime [4].”
The analytic bootstrap and AdS superhorizon locality (2012, result): “Note added: after this work was completed we learned of the related work of Komargodski and Zhiboedov [31]; they obtain very similar results using somewhat different methods.”
The (2, 0) superconformal bootstrap (2015, background): “To get a handle on (C13) we follow [57,58] and consider the series expansion around z̄ 1⁄4 0.”
A Mellin space approach to the conformal bootstrap (2016, methodology): “Furthermore, there are also certain analytic results available at large spin [14, 15, 16, 17].”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, background): “For example, the conformal blocks in the limits of large τ , ` or d [80–86], and subleading corrections to these, should be derivable using properties of AdS propagators.”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, unknown): “(See, however, [3, 44–48].”
Loops in AdS from conformal field theory (2016, methodology): “Note that γ (1) 0,`→∞ ∼ −2C 2 OOO` −2, consistent with the lightcone bootstrap [35, 36] (cf.”
Light-ray operators in conformal field theory (2018, background): “htcone bootstrap and large-spin perturbation theory [17–26, 79]. Lorentzian inversion formulae make it particularly simple to study OPE coeﬃcients and anomalous dimensions of “double-twist operators” [17, 18] and averaged OPE data for “multi-twist” operators (see e.g. [94, 95]). An important problem”
Bootstrapping the 3d Ising twist defect (2013, background): “It would be interesting to understand the asymptotic properties of the spectrum along the lines of [7, 9].”
The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, background): “An interesting feature of this argument (not realized in [59, 60], but pointed out in [61]) is that it most naturally determines a function h(h) instead of τ(`).”