More on analytic bootstrap for O(N) models

Dey, Parijat; Kaviraj, Apratim; Sen, Kallol

doi:10.1007/jhep06(2016)136

Cited by 36 publications

(37 citation statements)

References 73 publications

(135 reference statements)

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“…The Regge limit implies that the calculation is valid for n, l ≫ 1. These anomalous dimensions have been subsequently verified in [26,[62][63][64][65][66][67][68][69][70].…”

Section: Introductionmentioning

confidence: 71%

Black holes and conformal Regge bootstrap

Karlsson

Kulaxizi

Parnachev

et al. 2019

J. High Energ. Phys.

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Highly energetic particles traveling in the background of an asymptotically AdS black hole experience a Shapiro time delay and an angle deflection. These quantities are related to the Regge limit of a heavy-heavy-light-light four-point function of scalar operators in the dual CFT. The Schwarzschild radius of the black hole in AdS units is proportional to the ratio of the conformal dimension of the heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power counts the number of stress tensors in the multi-stress tensor operators which contribute to the four-point function. In the cross-channel the four-point function is determined by the OPE coefficients and anomalous dimensions of the heavy-light double-trace operators. We explain how this data can be obtained and explicitly compute the first and second order terms in the expansion of the anomalous dimensions. We observe perfect agreement with known results in the lightcone limit, which were obtained by computing perturbative corrections to the energy eigenstates in AdS spacetimes.

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“…The Regge limit implies that the calculation is valid for n, l ≫ 1. These anomalous dimensions have been subsequently verified in [26,[62][63][64][65][66][67][68][69][70].…”

Section: Introductionmentioning

confidence: 71%

Black holes and conformal Regge bootstrap

Karlsson

Kulaxizi

Parnachev

et al. 2019

J. High Energ. Phys.

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“…• It should be possible to develop our methods for other twist operators O n, and extend the holographic reconstruction calculations of [42,18] to arbitrary dimensions (see [41,46] for related earlier work on this). We believe that Mellin space techniques are the best suited to address this issue and our methods will prove useful in this venture.…”

Section: Discussionmentioning

confidence: 99%

Simplifying large spin bootstrap in Mellin space

Dey

Ghosh

Sinha

2018

J. High Energ. Phys.

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We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials, we derive explicit expressions as an asymptotic expansion in inverse conformal spin to any order, reproducing the contribution of any primary operator and its descendants in the crossed channel. The expressions are in terms of known mathematical functions and involve generalized Bernoulli (Nørlund) polynomials and the Mack polynomials and enable us to derive certain universal properties. Comparing with the recently introduced reformulated equations in terms of crossing symmetric tree level exchange Witten diagrams, we show that to leading order in anomalous dimension but to all orders in inverse conformal spin, the equations are the same as in the conventional formulation. At the next order, the polynomial ambiguity in the Witten diagram basis is needed for the equivalence and we derive the necessary constraints for the same.

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“…In the Regge limit the identification for the light operators is (we use the superscript "LL" below) which can also be obtained using conformal bootstrap [50][51] (see also [52][53][54][55][56][57][58]).…”

Section: Phase Shift and Anomalous Dimensionsmentioning

confidence: 99%

Black holes, heavy states, phase shift and anomalous dimensions

2019

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We compute the phase shift of a highly energetic particle traveling in the background of an asymptotically AdS black hole. In the dual CFT, the phase shift is related to a four point function in the Regge limit. The black hole mass is translated to the ratio between the conformal dimension of a heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power measures the number of stress tensors appearing in the intermediate channel. We compute the leading term in the phase shift in a holographic CFT of arbitrary dimensionality using Conformal Regge Theory and observe complete agreement with the gravity result. In a two-dimensional CFT with a large central charge the heavy-heavy-light-light Virasoro vacuum block reproduces the gravity phase shift to all orders in the expansion parameter. We show that the leading order phase shift is related to the anomalous dimensions of certain double trace operators and verify this agreement using known results for the latter. We also perform a separate gravity calculation of these anomalous dimensions to second order in the expansion parameter and compare with the phase shift expansion.

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More on analytic bootstrap for O(N) models

Cited by 36 publications

References 73 publications

Black holes and conformal Regge bootstrap

Black holes and conformal Regge bootstrap

Simplifying large spin bootstrap in Mellin space

Black holes, heavy states, phase shift and anomalous dimensions

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