The leading trajectory in the 2+1D Ising CFT

Caron-Huot, Simon; Gobeil, Yan; Zahraee, Zahra

doi:10.48550/arxiv.2007.11647

Cited by 29 publications

(54 citation statements)

References 47 publications

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“…This suggests that how random the CLLH truly are could also be theory dependent. A similar observation was made in [61].…”

Section: A Density Of States In the Tripled Spacesupporting

confidence: 85%

Generalized Spectral Form Factors and the Statistics of Heavy Operators

Belin¹,

Boer²,

Nayak³

et al. 2021

Preprint

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The spectral form factor is a powerful probe of quantum chaos that diagnoses the statistics of energy levels, but is blind to other features of a theory such as matrix elements of operators or OPE coefficients in conformal field theories. In this paper, we introduce generalized spectral form factors: new probes of quantum chaos sensitive to the dynamical data of a theory. These quantities can be studied using an effective theory of quantum chaos. We focus our attention on a particular combination of heavy-heavy-heavy OPE coefficients that generalizes the genus-2 partition function of two-dimensional CFTs, for which we define a spectral form factor. We probe the statistics of heavy-heavy-heavy OPE coefficients and confirm the OPE Randomness Hypothesis: these coefficients have a random matrix component in the ergodic regime. The EFT of quantum chaos predicts that the genus-2 spectral form factor displays a ramp and a plateau. Our results suggest that this is a common property of generalized spectral form factors. E-mail: a.belin [at] cern.ch, j.deboer [at] uva.nl, pranjal.nayak [at] unige.ch, julian.sonner [at] unige.ch Contents 4 EFT for the Genus-2 Spectral Form Factor 19

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“…This suggests that how random the CLLH truly are could also be theory dependent. A similar observation was made in [61].…”

Section: A Density Of States In the Tripled Spacesupporting

confidence: 85%

Generalized Spectral Form Factors and the Statistics of Heavy Operators

Belin¹,

Boer²,

Nayak³

et al. 2021

Preprint

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“…For example, by studying the Regge limit of the four-point function, one can obtain an OPE density weighted by a sine-squared function which suppresses the contributions near double-trace operators. The behavior of this density is then strongly affected by the Regge intercept of the CFT [59]. In particular, there appears to be an important qualitative difference between theories that saturate the Regge-intercept bound and have J 0 = 1 where the OPE coefficients can consistently be taken to be random, and theories with J 0 < 1 where the OPE coefficients must be peaked near double-trace operators and thus can not consistently be approximated as random variables.…”

Section: Lorentzian Limitmentioning

confidence: 99%

OPE statistics from higher-point crossing

Anous,

Belin,

de Boer

et al. 2021

Preprint

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We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These formulas involve products of four or more coefficients and include light-light-heavy as well as heavy-heavy-heavy contributions. They are derived from crossing symmetry of the six and higher point functions on the plane and should be interpreted as non-Gaussianities in the statistical distribution of the OPE coefficients. We begin with a formula for arbitrary operator exchanges (not necessarily primary) valid in any dimension. This is the first asymptotic formula constraining heavy-heavy-heavy OPE coefficients in d > 2. For two-dimensional CFTs, we present refined asymptotic formulas stemming from exchanges of quasi-primaries as well as Virasoro primaries.

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“…In this case the conformal blocks simplify considerably because the exchanged operator must be the external one. The block simplifies to a product of a two-and threepoint function, check (19) and (20). Thus, we conclude that the first terms in the lightcone limit in the channel (12) (34) are given by…”

Section: Five-point Functionmentioning

confidence: 81%

“…This large spin expansion is actually convergent up to a low spin value determined by the Regge behaviour of the four-point function [18,19]. A remarkable check of the accuracy of this method was done in the 3D Ising model where the numerical bootstrap provided the data for comparison [3,20] (see also [21] for the O(2) model). Motivated by this success, our goal is to extend the lightcone bootstrap to the case of higher-point functions and therefore access OPE data involving spinning operators.…”

Section: Introductionmentioning

confidence: 99%

Lightcone Bootstrap at higher points

Antunes,

Costa,

Goncalves

et al. 2021

Preprint

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Higher-point functions of scalar operators are a rich observable in CFTs, as they contain OPE data involving multiple spinning operators. We derive the lightcone blocks for five-and six-point functions in the snowflake channel and use them to bootstrap these correlators in the lightcone limit. As a result we determine the large spin expansion of OPE coefficients involving two or three spinning operators. We verify our results by comparing to the block decomposition of higher-point functions in generalized free theory and in theories with a cubic coupling.

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The leading trajectory in the 2+1D Ising CFT

Cited by 29 publications

References 47 publications

Generalized Spectral Form Factors and the Statistics of Heavy Operators

Generalized Spectral Form Factors and the Statistics of Heavy Operators

OPE statistics from higher-point crossing

Lightcone Bootstrap at higher points

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