Bootstrap and amplitudes: a hike in the landscape of quantum field theory

Elvang, Henriette

doi:10.1088/1361-6633/abf97e

Cited by 11 publications

(10 citation statements)

References 94 publications

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“…The structure of scattering amplitudes beyond Feynman diagrams has undergone intense study in several contexts over the past 60 years. This program has been very successful at tree level, where numerous bottom-up approaches have almost completely circumvented the Lagrangian approach [12,13,15,[112][113][114][115][116][117]. However, a systematic understanding of how locality, causality and unitarity are precisely encoded at all orders in scattering amplitudes remains surprisingly elusive.…”

Section: Discussionmentioning

confidence: 99%

“…Significant strides have been made in both understanding the underlying structure of amplitudes and developing new computation methods. Many techniques for computing amplitudes are under active research, such as the double copy [2][3][4], positive geometry [5][6][7], intersection theory [8][9][10] and much more [11][12][13][14][15][16][17][18]. In particular, a number of techniques have emerged that leverage non-perturbative properties of the S-matrix, such as unitarity and cluster decomposition.…”

Section: Jhep07(2021)049mentioning

confidence: 99%

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Algebraic branch points at all loop orders from positive kinematics and wall crossing

Herderschee

2021

J. High Energ. Phys.

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There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar $$ \mathcal{N} $$ N = 4 SYM. A long-standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

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Section: Discussionmentioning

confidence: 99%

Section: Jhep07(2021)049mentioning

confidence: 99%

Algebraic branch points at all loop orders from positive kinematics and wall crossing

Herderschee

2021

J. High Energ. Phys.

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“…in refs. [22,25,59,60] and references therein. The following two paragraphs give a brief working introduction to soft bootstrap techniques.…”

Section: Soft Bootstrapmentioning

confidence: 99%

Nonrelativistic effective field theories with enhanced symmetries and soft behavior

Mojahed

Brauner

2022

J. High Energ. Phys.

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We systematically explore the landscape of nonrelativistic effective field theories with a local S-matrix and enhanced symmetries and soft behavior. The exploration is carried out using both conventional quantum field theory methods based on symmetry arguments, and recently developed on-shell recursion relations. We show that, in contrary to relativistic theories, enhancement of the soft limit of scattering amplitudes in nonrelativistic theories is generally not a byproduct of symmetry alone, but requires additional low-energy data. Sufficient conditions for enhanced scattering amplitudes can be derived by combining symmetries and dispersion relations of the scattered particles. This has direct consequences for the infrared dynamics that different types of nonrelativistic Nambu-Goldstone bosons can exhibit. We then use a bottom-up soft bootstrap approach to narrow down the landscape of nonrelativistic effective field theories that possess a consistent low-energy S-matrix. We recover two exceptional theories of a complex Schrödinger-type scalar, namely the ℂP1 nonlinear sigma model and the Schrödinger-Dirac-Born-Infeld theory. Moreover, we use soft recursion to prove a no-go theorem ruling out the existence of other exceptional Schrödinger-type theories. We also prove that all exceptional theories of a single real scalar with a linear dispersion relation are necessarily Lorentz-invariant. Soft recursion allows us to obtain some further general bounds on the landscape of nonrelativistic effective theories with enhanced soft limits. Finally, we present a novel theory of a complex scalar with a technically natural quartic dispersion relation. Altogether, our work represents the first step of a program to extend the developments in the study of scattering amplitudes to theories without Lorentz invariance.

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“…• Going beyond two-point and three-point amplitudes, a resummation over the field expansion will leave us with a non-trivial derivative expansion [149]. Nevertheless, the derivative expansion can still be systematically organized through the use of group theoretical techniques [148,150].…”

Section: Impact Of Kinematic Cutsmentioning

confidence: 99%

Unitarity Bounds on Effective Field Theories at the LHC

Cohen,

Doss,

2021

Preprint

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Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables e.g. cross sections with partonic center-of-mass energy √ ŝ as a systematically improvable expansion suppressed by a new physics scale M . If one is interested in EFT predictions in the parameter space where M < √ ŝ, concerns of self-consistency emerge, which can manifest as a violation of partial-wave unitarity. However, when we search for the effects of an EFT at a hadron collider with centerof-mass energy √ s using an inclusive strategy, we typically do not have access to the event-by-event value of √ ŝ. This motivates the need for a formalism that incorporates parton distribution functions into the partial-wave unitarity analysis. Developing such a framework and initiating an exploration of its implications is the goal of this work. Our approach opens up a potentially valid region of the EFT parameter space where M √ s. We provide evidence that there exist valid EFTs in this parameter space. The unitarity bounds are sensitive to the details of a given search, an effect we investigate by varying kinematic cuts.

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Bootstrap and amplitudes: a hike in the landscape of quantum field theory

Cited by 11 publications

References 94 publications

Algebraic branch points at all loop orders from positive kinematics and wall crossing

Algebraic branch points at all loop orders from positive kinematics and wall crossing

Nonrelativistic effective field theories with enhanced symmetries and soft behavior

Unitarity Bounds on Effective Field Theories at the LHC

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