Extremal effective field theories

Caron-Huot, Simon; Duong, Vincent Van

doi:10.1007/jhep05(2021)280

Cited by 156 publications

(378 citation statements)

References 32 publications

(45 reference statements)

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“…One interesting point to make note of is the following: for a ∼ 0, for the above condition to hold, we will need µ 1 µ 2 < 0. This is a consequence of unitarity and conforms with the signs in [11]. We leave a detailed investigation of such constraints for the future 15 .…”

Section: A Toy Example: Scalar Eft Approximationsupporting

confidence: 78%

“…. Compared to [10,11], the lower bound is identical but the upper bound we quote above is stronger. We have checked this inequality for several known examples.…”

Section: Introductionmentioning

confidence: 82%

“…Using eq. (63), it is also possible to deduce bounds [29] on the individual W 0,2 /W 1,0 , W 1,1 /W 1,0 , W 2,0 /W 1,0 and these appear comparable to [11].…”

Section: Bounds On {α N (A)}mentioning

confidence: 99%

“…For starters, the amplitudes we consider below are in two "standard" forms. Both of these were considered in [11] to study scalar EFTs, and it was found that scalar EFTs could be approximated as a convex sum of the amplitudes below. Thus consider the sum…”

Section: A Toy Example: Scalar Eft Approximationmentioning

confidence: 99%

“…Over the last few months, the existence of upper and lower bounds on ratios of Wilson coefficients have been discovered [4,10,11]. These bounds are remarkable since they say that Wilson coefficients cannot be arbitrarily big or small and, in a sense, corroborate the efficacy of effective field theories.…”

Section: Introductionmentioning

confidence: 99%

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Quantum field theory and the Bieberbach conjecture

2021

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An intriguing correspondence between ingredients in geometric function theory related to the famous Bieberbach conjecture (de Branges’ theorem) and the non-perturbative crossing symmetric representation of 2-2 scattering amplitudes of identical scalars is pointed out. Using the dispersion relation and unitarity, we are able to derive several inequalities, analogous to those which arise in the discussions of the Bieberbach conjecture. We derive new and strong bounds on the ratio of certain Wilson coefficients and demonstrate that these are obeyed in one-loop \phi^4ϕ4 theory, tree level string theory as well as in the S-matrix bootstrap. Further, we find two sided bounds on the magnitude of the scattering amplitude, which are shown to be respected in all the contexts mentioned above. Translated to the usual Mandelstam variables, for large |s||s|, fixed tt, the upper bound reads |\mathcal{M}(s,t)|\lesssim |s^2||ℳ(s,t)|≲|s2|. We discuss how Szeg"{o}’s theorem corresponds to a check of univalence in an EFT expansion, while how the Grunsky inequalities translate into nontrivial, nonlinear inequalities on the Wilson coefficients.

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Section: A Toy Example: Scalar Eft Approximationsupporting

confidence: 78%

“…. Compared to [10,11], the lower bound is identical but the upper bound we quote above is stronger. We have checked this inequality for several known examples.…”

Section: Introductionmentioning

confidence: 82%

“…Using eq. (63), it is also possible to deduce bounds [29] on the individual W 0,2 /W 1,0 , W 1,1 /W 1,0 , W 2,0 /W 1,0 and these appear comparable to [11].…”

Section: Bounds On {α N (A)}mentioning

confidence: 99%

Section: A Toy Example: Scalar Eft Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum field theory and the Bieberbach conjecture

2021

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Crossing antisymmetric Polyakov blocks + dispersion relation

Kaviraj

2022

J. High Energ. Phys.

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Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the ‘+ type Polyakov blocks’. These blocks are built from AdSd+1 Witten diagrams. In 1d they encode the ‘+ type’ analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent ‘locality constraints’ in addition to the usual CFT sum rules given by the ‘Polyakov conditions’. We use the Polyakov blocks to simplify more general analytic functionals in d > 1 and global symmetry functionals.

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Spinning S-matrix bootstrap in 4d

Hebbar

Karateev

Penedones

2022

J. High Energ. Phys.

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We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.

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Extremal effective field theories

Cited by 156 publications

References 32 publications

Quantum field theory and the Bieberbach conjecture

Quantum field theory and the Bieberbach conjecture

Crossing antisymmetric Polyakov blocks + dispersion relation

Spinning S-matrix bootstrap in 4d

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