Fast conformal bootstrap and constraints on 3d gravity

Afkhami-Jeddi, Nima; Hartman, Thomas; Tajdini, Amirhossein

doi:10.1007/jhep05(2019)087

Cited by 76 publications

(114 citation statements)

References 56 publications

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“…Extending this success, the modern modular bootstrap program has been developed to study, among others, a medium temperature expansion of the torus partition function and its consistency with modular invariance. It generalizes the Cardy constraints on the heavy operators to, in particular, the gap and degeneracies in the spectrum in any 2d CFT [30][31][32][33][34][35][36]. It has been proven that the lightest primary operator above the vacuum is universally bounded from above by c 6 + 0.474 for all c > 1 CFTs [30].…”

Section: Modular Bootstrapmentioning

confidence: 80%

“…It has been proven that the lightest primary operator above the vacuum is universally bounded from above by c 6 + 0.474 for all c > 1 CFTs [30]. In the large c limit, this bound has recently been improved to c 9.1 + O(1) [36]. In the presence of a Z 2 topological defect line L, we can consider torus partition functions with L extending along the time or spatial direction, which we denote as Z L (τ,τ ) and Z L (τ,τ ), respectively.…”

Section: Modular Bootstrapmentioning

confidence: 99%

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Anomalies and bounds on charged operators

2019

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We study the implications of 't Hooft anomaly (i.e. obstruction to gauging) on conformal field theory, focusing on the case when the global symmetry is Z 2 . Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal Z 2 global symmetry are derived. The bootstrap bounds depend dramatically on the 't Hooft anomaly. In particular, there is a universal upper bound on the lightest Z 2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous. In the non-anomalous case, we find that the lightest Z 2 odd state and the defect ground state cannot both be arbitrarily heavy. We also consider theories with a U (1) global symmetry, and comment that there is no bound on the lightest U (1) charged operator if the symmetry is non-anomalous.

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Section: Modular Bootstrapmentioning

confidence: 80%

Section: Modular Bootstrapmentioning

confidence: 99%

Anomalies and bounds on charged operators

2019

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“…This bound has since been improved numerically as well as analytically in various ways [9][10][11][12][13][14][15], in particular using the linear programming method introduced in [16]. So far, in the large-c limit the best analytic bound is [13] ∆ 0 ≤ c/8.503, while the numerical upper bound, obtained by extrapolating large-c data, is [12] ∆ 0 ≤ c/9.08. Other bounds can be found by assuming complete factorization of the partition function into a holomorphic and an antiholomorphic part [17].…”

Section: Introductionmentioning

confidence: 99%

Modular bootstrap, elliptic points, and quantum gravity

Gliozzi

2020

Phys. Rev. Research

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The modular bootstrap program for two-dimensional conformal field theories could be seen as a systematic exploration of the physical consequences of consistency conditions at the elliptic points and at the cusp of their torus partition function. The study at τ = i, the elliptic point stabilized by the modular inversion S, was initiated by Hellerman, who found a general upper bound for the most relevant scaling dimension ∆. Likewise, analyticity at τ = i∞, the cusp stabilized by the modular translation T , yields an upper bound on the twist gap. Here we study consistency conditions at τ = exp[2iπ/3], the elliptic point stabilized by S T . We find a much stronger upper bound in the large-c limit, namely ∆ < c−1 12 + 0.092, which is very close to the minimal mass threshold of the BTZ black holes in the gravity dual of AdS3/CF T2 correspondence.

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“…The simplest (though by no means the only) set of constraints on the gap arise from modular invariance of the CFT partition function. This is the "modular bootstrap" program pioneered by Hellerman [4] and pursued by several authors [5][6][7].…”

Section: Jhep12(2019)048mentioning

confidence: 99%

Sphere packing and quantum gravity

Hartman

Mazáč

Rastelli

2019

J. High Energ. Phys.

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101

154

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We establish a precise relation between the modular bootstrap, used to constrain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra U(1) c maps exactly to the Cohn-Elkies linear programming bound on the sphere packing density in d = 2c dimensions. We also show that the analytic functionals developed earlier for the correlator conformal bootstrap can be adapted to this context. For c = 4 and c = 12, these functionals exactly reproduce the "magic functions" used recently by Viazovska [1] and Cohn et al. [2] to solve the sphere packing problem in dimensions 8 and 24. The same functionals are also applied to general 2D CFTs, with only Virasoro symmetry. In the limit of large central charge, we relate sphere packing to bounds on the black hole spectrum in 3D quantum gravity, and prove analytically that any such theory must have a nontrivial primary state of dimension ∆ 0 c/8.503.

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Fast conformal bootstrap and constraints on 3d gravity

Cited by 76 publications

References 56 publications

Anomalies and bounds on charged operators

Anomalies and bounds on charged operators

Modular bootstrap, elliptic points, and quantum gravity

Sphere packing and quantum gravity

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