More analytic bootstrap: nonperturbative effects and fermions

Albayrak, Soner; Meltzer, David O.; Poland, David

doi:10.1007/jhep08(2019)040

Cited by 53 publications

(109 citation statements)

References 55 publications

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“…When the external scalars have identical scaling dimensions, we also provided the expression (27) for the Lorentzian inversion of a general cross-channel conformal block, which will be particularly useful for the investigations in d = 1, 2, 4 dimensions, as general compact expressions were not available in the past. They include the analytic conformal bootstrap of the Wilson-Fisher fixed points [37,42], conformal field theories in d = 3 dimensions [40,43] and d > 4 dimensions [15].…”

Section: Resultsmentioning

confidence: 99%

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Closed-form expression for cross-channel conformal blocks near the lightcone

2020

J high energy phys

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In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of generic scalars. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose the natural basis functions for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampé de Fériet function, which applies to intermediate operators of arbitrary spin in general dimensions. We also derive the general Lorentzian inversion for the case of identical external scaling dimensions. Our approach and results may shed light on the complete analytic structure of conformal blocks.

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Section: Resultsmentioning

confidence: 99%

“…The choice of n depends on the required precision. Our formula (27) can efficiently reproduce the 3d nonperturbative results in [40], which were obtained by decomposing 3d conformal blocks into 2d blocks [41].…”

Section: Identical External Scaling Dimensionsmentioning

confidence: 99%

Closed-form expression for cross-channel conformal blocks near the lightcone

2020

J high energy phys

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“…The problem above is closely related to crossing kernels and 6j symbols [31][32][33][34][35][36]. In [33] expressions were given for the leading order anomalous dimension of a double-field operator from a generic operator in the crossed channel.…”

Section: Relation To Crossing Kernelsmentioning

confidence: 99%

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

2020

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We apply the methods of modern analytic bootstrap to the critical O(N ) model in a 1/N expansion. At infinite N the model possesses higher spin symmetry which is weakly broken as we turn on 1/N . By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order 1/N , and the CFT-data for the non-singlet currents to order 1/N 2 . To order 1/N our results are in perfect agreement with those in the literature. To order 1/N 2 we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge C J to this order.

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“…We thank David Poland for discussions on this point. See[61][62][63][64][65] for examples of this phenomena 18. Conserved spin-1 currents and the stress-tensor cannot appear in this OPE.…”

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confidence: 99%

Higher spin ANEC and the space of CFTs

Meltzer

2019

J. High Energ. Phys.

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We study the positivity properties of the leading Regge trajectory in higher-dimensional, unitary, conformal field theories (CFTs). These conditions correspond to higher spin generalizations of the averaged null energy condition (ANEC). By studying higher spin ANEC, we will derive new bounds on the dimensions of charged, spinning operators and prove that if the Hofman-Maldacena bounds are saturated, then the theory has a higher spin symmetry. We also derive new, general bounds on CFTs, with an emphasis on theories whose spectrum is close to that of a generalized free field theory. As an example, we consider the Ising CFT and show how the OPE structure of the leading Regge trajectory is constrained by causality. Finally, we use the analytic bootstrap to perform additional checks, in a large class of CFTs, that higher spin ANEC is obeyed at large and finite spin. In the process, we calculate corrections to large spin OPE coefficients to one-loop and higher in holographic CFTs.

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More analytic bootstrap: nonperturbative effects and fermions

Cited by 53 publications

References 55 publications

Closed-form expression for cross-channel conformal blocks near the lightcone

Closed-form expression for cross-channel conformal blocks near the lightcone

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

Higher spin ANEC and the space of CFTs

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