Three ways to solve critical ϕ4 theory on 4 − 𝜖 dimensional real projective space: Perturbation, bootstrap, and Schwinger–Dyson equation

Hasegawa, Chika; Nakayama, Yu

doi:10.1142/s0217751x18500495

Cited by 16 publications

(19 citation statements)

References 67 publications

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“…The OPE coefficients f φφ[φφ] 0 (J) and anomalous dimensions γ(J) can be computed using the lightcone bootstrap for vacuum four-point functions [30][31][32][33][34][35][36][37]. 7 Our precise result is that the two sides of (1.5) match to all orders in an expansion in 1/J. (Our inversion formula also produces nonperturbative corrections in J.)…”

Section: Introductionmentioning

confidence: 99%

“…They can be thought of schematically as [φφ] 0,J = φ∂ µ1 · · · ∂ µ J φ. 7 Note that [31] uses the convention c O = (− 1 2 ) J O .…”

Section: Introductionmentioning

confidence: 99%

“…See appendix D for a discussion of subtleties that can arise in compactification on S 1 and other manifolds. See[5][6][7] for previous work on the bootstrap in d > 2 on nontrivial manifolds.…”

mentioning

confidence: 99%

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The conformal bootstrap at finite temperature

Iliesiu

Kologlu

Mahajan

et al. 2018

J. High Energ. Phys.

104

158

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We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one-and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal onepoint functions for all higher-spin currents in the critical O(N ) model at leading order in 1/N . Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.

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Section: Introductionmentioning

confidence: 99%

“…They can be thought of schematically as [φφ] 0,J = φ∂ µ1 · · · ∂ µ J φ. 7 Note that [31] uses the convention c O = (− 1 2 ) J O .…”

Section: Introductionmentioning

confidence: 99%

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The conformal bootstrap at finite temperature

Iliesiu

Kologlu

Mahajan

et al. 2018

J. High Energ. Phys.

104

158

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show abstract

“…See for instance[43][44][45][46][47][48][49][50][51] or for supersymmetric studies. Other analysis can also be found in[75][76][77][78][79][80][81].…”

mentioning

confidence: 99%

Carving out OPE space and precise O(2) model critical exponents

Chester

Landry

Liu

et al. 2020

J. High Energ. Phys.

156

217

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We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.

show abstract

“…See for instance[43][44][45][46][47][48][49][50][51] or for supersymmetric studies. Other analysis can also be found in[75][76][77][78][79][80][81].…”

mentioning

confidence: 99%

Carving out OPE space and precise $O(2)$ model critical exponents

Chester,

Landry,

Liu

et al. 2019

Preprint

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Three ways to solve critical ϕ4 theory on 4 − 𝜖 dimensional real projective space: Perturbation, bootstrap, and Schwinger–Dyson equation

Cited by 16 publications

References 67 publications

The conformal bootstrap at finite temperature

The conformal bootstrap at finite temperature

Carving out OPE space and precise O(2) model critical exponents

Carving out OPE space and precise $O(2)$ model critical exponents

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