The Gross-Neveu-Yukawa archipelago

Erramilli, Rajeev S.; Iliesiu, Luca V.; Kravchuk, Petr; Liu, Aike; Poland, David; Simmons-Duffin, David

doi:10.1007/jhep02(2023)036

Cited by 23 publications

(6 citation statements)

References 80 publications

(235 reference statements)

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“…So far, the conformal bootstrap has mostly been applied to four-point correlation functions with external scalar operators (see [5][6][7][8][9][10][11][12][13] for some exceptions). Therefore, most of the known OPE coefficients involve two scalars and one spinning operator.…”

Section: Introductionmentioning

confidence: 99%

The five-point bootstrap

Poland,

Prilepina,

Tadić

2023

J. High Energ. Phys.

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We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators 〈σσϵσσ〉 in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We then compute several OPE coefficients involving ϵ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

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Section: Introductionmentioning

confidence: 99%

The five-point bootstrap

Poland,

Prilepina,

Tadić

2023

J. High Energ. Phys.

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“…When this space is cut down to a manageable size, it can be searched with the numerical bootstrap [15]. In the most favourable cases, one can force the theory of interest to live in an "island" by rigorously excluding the possibility that a consistent CFT lives at any of the surrounding points [70][71][72][73][74][75]. More commonly, a precursor to this type of result called a "kink" is what…”

Section: Numerical Resultsmentioning

confidence: 99%

Analytic and numerical bootstrap for the long-range Ising model

Behan,

Lauria,

Nocchi

et al. 2024

J. High Energ. Phys.

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We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI.

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“…and for present purposes we consider the Lagrangian For reduction to three dimensions a convenient basis is obtained by taking γ µ → γµ with, adapting [86,90,91],…”

Section: A Majorana Fermions and Their Reductionmentioning

confidence: 99%

Explorations in Scalar Fermion Theories: $β$-functions, Supersymmetry and Fixed Points

Jack¹,

Osborn²,

Steudtner³

2023

Preprint

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Results for β-functions and anomalous dimensions in general scalar fermion theories are presented to three loops. Various constraints on the individual coefficients for each diagram following from supersymmetry are analysed. The results are used to discuss potential fixed points in the ε-expansion for scalar fermion theories, with arbitrary numbers of scalar fields, and where there are just two scalar couplings and one Yukawa coupling. For different examples the fixed points follow a similar pattern as the numbers of fermions is varied. For diagrams with subdivergences there are extensive consistency constraints arising from the existence of a perturbative a-function and these are analysed in detail. Further arbitrary scheme variations which preserve the form of β functions and anomalous dimensions in terms of 1PI diagrams are also discussed. The existence of linear and quadratic scheme invariants is demonstrated and the consistency condition are shown to be expressible in terms of these invariants.

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The Gross-Neveu-Yukawa archipelago

Cited by 23 publications

References 80 publications

The five-point bootstrap

The five-point bootstrap

Analytic and numerical bootstrap for the long-range Ising model

Explorations in Scalar Fermion Theories: $β$-functions, Supersymmetry and Fixed Points

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