scholarly journals Constraining the weights of Stokes polytopes using BCFW recursions for ϕ4

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Ishan Srivastava
Keyword(s):  
Scattering Amplitudes ◽  
Great Depth ◽  
Tree Level ◽  
Recursion Relations ◽  
3 Dimensional ◽  
Loop Level ◽  
Boundary Terms ◽  
Geometric Objects ◽  
The Relationship ◽  
Geometric Formulation

Abstract The relationship between certain geometric objects called polytopes and scattering amplitudes has revealed deep structures in QFTs. It has been developed in great depth at the tree- and loop-level amplitudes in $$ \mathcal{N} $$ N = 4 SYM theory and has been extended to the scalar ϕ3 and ϕ4 theories at tree-level. In this paper, we use the generalized BCFW recursion relations for massless planar ϕ4 theory to constrain the weights of a class of geometric objects called Stokes polytopes, which manifest in the geometric formulation of ϕ4 amplitudes. We see that the weights of the Stokes polytopes are intricately tied to the boundary terms in ϕ4 theories. We compute the weights of N = 1, 2, and 3 dimensional Stokes polytopes corresponding to six-, eight- and ten-point amplitudes respectively. We generalize our results to higher-point amplitudes and show that the generalized BCFW recursions uniquely fix the weights for an n-point amplitude.

scholarly journals Plahte diagrams for string scattering amplitudes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Pongwit Srisangyingcharoen ◽  
Paul Mansfield
Keyword(s):  
Scattering Amplitudes ◽  
Analytic Continuation ◽  
Complex Plane ◽  
Open String ◽  
Tree Level ◽  
Recursion Relations ◽  
Sign Changes ◽  
String Amplitudes

Abstract Plahte identities are monodromy relations between open string scattering amplitudes at tree level derived from the Koba-Nielsen formula. We represent these identities by polygons in the complex plane. These diagrams make manifest the appearance of sign changes and singularities in the analytic continuation of amplitudes. They provide a geometric expression of the KLT relations between closed and open string amplitudes. We also connect the diagrams to the BCFW on-shell recursion relations and generalise them to complex momenta resulting in a relation between the complex phases of partial amplitudes.

scholarly journals Weights, recursion relations and projective triangulations for positive geometry of scalar theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Renjan Rajan John ◽  
Ryota Kojima ◽  
Sujoy Mahato
Keyword(s):  
Scattering Amplitudes ◽  
Detailed Analysis ◽  
Tree Level ◽  
Massless Scalar ◽  
Weighted Sum ◽  
Canonical Forms ◽  
Factorization Property ◽  
Scalar Theory ◽  
Recursion Relations ◽  
Scalar Theories

Abstract The story of positive geometry of massless scalar theories was pioneered in [1] in the context of bi-adjoint ϕ3 theories. Further study proposed that the positive geometry for a generic massless scalar theory with polynomial interaction is a class of polytopes called accordiohedra [2]. Tree-level planar scattering amplitudes of the theory can be obtained from a weighted sum of the canonical forms of the accordiohedra. In this paper, using results of the recent work [3], we show that in theories with polynomial interactions all the weights can be determined from the factorization property of the accordiohedron. We also extend the projective recursion relations introduced in [4, 5] to these theories. We then give a detailed analysis of how the recursion relations in ϕp theories and theories with polynomial interaction correspond to projective triangulations of accordiohedra. Following the very recent development [6] we also extend our analysis to one-loop integrands in the quartic theory.

scholarly journals Gravity loop integrands from the ultraviolet

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Alex Edison ◽  
Enrico Herrmann ◽  
Julio Parra-Martinez ◽  
Jaroslav Trnka
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Space ◽  
Indirect Evidence ◽  
Tree Level ◽  
Large Momentum ◽  
Recursion Relations ◽  
Yang Mills ◽  
The One ◽  
Geometric Picture ◽  
Super Yang Mills Theory

We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.

scholarly journals Propagators, BCFW recursion and new scattering equations at one loop

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Joseph A. Farrow ◽  
Yvonne Geyer ◽  
Arthur E. Lipstein ◽  
Ricardo Monteiro ◽  
Ricardo Stark-Muchão
Keyword(s):  
Gauge Theory ◽  
Tree Level ◽  
Loop Momentum ◽  
Planar Case ◽  
Linear Type ◽  
Recursion Relations ◽  
Loop Level ◽  
Alternative Approach ◽  
Forward Limit ◽  
Limit Procedure

Abstract We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part of the paper, we revisit the BCFW construction of one-loop integrands in momentum space, using a convenient parametrisation of the D-dimensional loop momentum. We work out explicit examples with and without supersymmetry, and discuss the non-planar case in both gauge theory and gravity. In the second part of the paper, we study an alternative approach to one-loop integrands, where these are written as worldsheet formulas based on new one-loop scattering equations. These equations, which are inspired by BCFW, lead to standard Feynman-type propagators, instead of the ‘linear’-type loop-level propagators that first arose from the formalism of ambitwistor strings. We exploit the analogies between the two approaches, and present a proof of an all-multiplicity worldsheet formula using the BCFW recursion.

scholarly journals Simplicity of AdS supergravity at one loop

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Luis F. Alday ◽  
Xinan Zhou
Keyword(s):  
Closed Form ◽  
Conformal Symmetry ◽  
Flat Space ◽  
Tree Level ◽  
Loop Level ◽  
Level Data ◽  
Space Limit ◽  
Loop Amplitude

Abstract We demonstrate the simplicity of AdS5× S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the $$ \left\langle {\mathcal{O}}_2^{SG}{\mathcal{O}}_2^{SG}{\mathcal{O}}_p^{SG}{\mathcal{O}}_p^{SG}\right\rangle $$ O 2 SG O 2 SG O p SG O p SG correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.

scholarly journals Open associahedra and scattering forms

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Aidan Herderschee ◽  
Fei Teng
Keyword(s):  
Scattering Amplitudes ◽  
Canonical Form ◽  
Recursion Relations ◽  
Fiber Product ◽  
New Phenomena

Abstract We continue the study of open associahedra associated with bi-color scattering amplitudes initiated in ref. [1]. We focus on the facet geometries of the open associahedra, uncovering many new phenomena such as fiber-product geometries. We then provide novel recursion procedures for calculating the canonical form of open associahedra, generalizing recursion relations for bounded polytopes to unbounded polytopes.

TREE DIAGRAMS IN WITTEN’S SUPERSTRING FIELD THEORY

1989 ◽  
Vol 04 (21) ◽  
pp. 2063-2071
Author(s):  
GEORGE SIOPSIS
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Invariant Theory ◽  
Higher Order ◽  
Contact Term ◽  
Tree Level ◽  
Gauge Invariant

It is shown that the contact term discovered by Wendt is sufficient to ensure finiteness of all tree-level scattering amplitudes in Witten’s field theory of open superstrings. Its inclusion in the action also leads to a gauge-invariant theory. Thus, no additional higher-order counterterms in the action are needed.

scholarly journals Composing effective prediction at five points

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Laurentiu Rodina ◽  
Suna Zekioğlu
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitude ◽  
Building Blocks ◽  
Tree Level ◽  
Critical Aspect ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Single Trace ◽  
The Relationship ◽  
Double Copy

Abstract Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

scholarly journals On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

scholarly journals Pola Asuh Orang Tua Terhadap Anak Berdasarkan Golongan Darah

2019 ◽  
Vol 4 (2) ◽  
pp. 114-129
Author(s):  
Hamam Burhanuddin
Keyword(s):  
Social Interaction ◽  
The Body ◽  
Blood Type ◽  
Relationship With God ◽  
3 Dimensional ◽  
Islamic Studies ◽  
Stage Of Development ◽  
Relationship Of ◽  
The Relationship ◽  
The Brain

The study in this paper are explain about the studies of medical (medicine) blood type have the same relationship to human character because the blood producing antibodies and antigens. It could determine a person helpless hold strong or weak body, has an allergy to something or not, in the blood also contains various nutrients (like protein) and also the oxygen being supplied to the brain and nerves and body affect performance someone will then be emanated from the attitude of the person and social interaction. As has been explained, but keep in mind, there is blood in the genes, the nature of which is carried in the body/genotif rightly so it is, but we can not ignore the fenotif/nature arising or visible, this trait appear due to interaction between genes and the environment, so even if the person is smart in the intelligentsia and emotional, but grew up in a bad environment is going to be a bad trait. The theory of personality based on blood type can be used as a reference in parenting children through an understanding of the fundamental principles of the application of personality accompanied by parenting. Furthermore, the taking of steps in the care tailored to the stage of development of the child, in the Qur'an explicitly did not mentioned paragraph that discusses about blood type, but in the Qur'an there are blood (ad-Dam), Islamic studies in the study of Children is seen as a mandate from God, forming 3-dimensional relationships, with parents as the central figure. First, her parents relationship with God that is backed by the presence of children. Second, the relationship of the child (which still need a lot of guidance) with God through his parents. Third, the relationship of the child with both parents under the tutelage and guidance of God.

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