scholarly journals $$ \mathcal{N} $$ = 7 On-shell diagrams and supergravity amplitudes in momentum twistor space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Connor Armstrong ◽  
Joseph A. Farrow ◽  
Arthur E. Lipstein
Keyword(s):  
Scattering Amplitudes ◽  
Twistor Space ◽  
Tree Level ◽  
Yang Mills

Abstract We derive an on-shell diagram recursion for tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 7 supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in momentum twistor space to non-MHV amplitudes. In particular, we recast five and six-point NMHV amplitudes in terms of $$ \mathcal{N} $$ N = 7 R-invariants analogous to those of $$ \mathcal{N} $$ N = 4 super-Yang-Mills, which makes cancellation of spurious poles more transparent. Above 5-points, this requires defining momentum twistors with respect to different orderings of the external momenta.

YANG-MILLS AMPLITUDES FROM STRING THEORY IN TWISTOR SPACE

2005 ◽  
Vol 20 (15) ◽  
pp. 3416-3419 ◽  
Author(s):  
MARCUS SPRADLIN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Twistor Space ◽  
Mathematical Structure ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Algebraic Equations ◽  
Yang Mills

Tree-level gluon scattering amplitudes in Yang-Mills theory frequently display simple mathematical structure which is completely obscure in the calculation of Feynman diagrams. We describe a novel way of calculating these amplitudes, motivated by a conjectured relation to twistor space, in which the problem of summing Feynman diagrams is replaced by the problem of solving a certain set of algebraic equations.

scholarly journals 10D super-Yang-Mills scattering amplitudes from its pure spinor action

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Maor Ben-Shahar ◽  
Max Guillen
Keyword(s):  
Scattering Amplitudes ◽  
Jacobi Identity ◽  
Gauge Condition ◽  
Tree Level ◽  
Pure Spinor ◽  
Yang Mills

Abstract Using the pure spinor master action for 10D super-Yang-Mills in the gauge b0V = QΞ, tree-level scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested b-ghost operators, and show that the Siegel gauge condition b0V = 0 gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from the Jacobi identity of a kinematic algebra.

scholarly journals PRODUCTION OF NON-ABELIAN TENSOR GAUGE BOSONS TREE AMPLITUDES AND BCFW RECURSION RELATION

2011 ◽  
Vol 26 (15) ◽  
pp. 2537-2555 ◽  
Author(s):  
GEORGE GEORGIOU ◽  
GEORGE SAVVIDY
Keyword(s):  
Scattering Amplitudes ◽  
High Spin ◽  
Recursion Relation ◽  
Coupling Constants ◽  
Tree Level ◽  
Taylor Formula ◽  
Coupling Constant ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Vector Bosons

The BCFW recursion relation is used to calculate tree-level scattering amplitudes in generalized Yang–Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons and high spin non-Abelian tensor gauge bosons are equal to the Yang–Mills coupling constant. We derive a generalization of the Parke–Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorphic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s = 1.

scholarly journals CONFORMAL INVARIANCE OF TENSOR BOSON TREE AMPLITUDES

2012 ◽  
Vol 27 (18) ◽  
pp. 1250103 ◽  
Author(s):  
IGNATIOS ANTONIADIS ◽  
GEORGE SAVVIDY
Keyword(s):  
Scattering Amplitudes ◽  
Conformal Invariance ◽  
Recursion Relation ◽  
Conformal Group ◽  
Tree Level ◽  
Unexpected Result ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Higher Spin

The BCFW recursion relation allows to find out the tree-level scattering amplitudes for gluons and tensor gauge bosons in generalized Yang–Mills theory. We demonstrate that the corresponding MHV amplitudes for the tensor gauge bosons of spin-s and n gluons are invariant under conformal group of transformations. This is highly unexpected result for the higher-spin particles, in particular this is not true for the scattering amplitudes of gravitons. We discuss and compare the tree-level scattering amplitudes for the charged tensor bosons with the corresponding scattering amplitudes for gravitons, stressing their differences and similarities.

Open and Closed Superstring Five-Point Amplitudes at Tree-Level

2003 ◽  
Vol 18 (12) ◽  
pp. 2127-2133 ◽  
Author(s):  
F. Brandt ◽  
F. Machado ◽  
R. Medina
Keyword(s):  
Scattering Amplitudes ◽  
Fundamental Constant ◽  
Zero Order ◽  
Tree Level ◽  
Superstring Theory ◽  
Yang Mills ◽  
First Case ◽  
Long Time ◽  
Superstring Theories ◽  
Hilbert Action

In this contribution the tree-level effective actions for gluons and gravitons, as derived from Open and Closed Superstring theories, are reviewed respectively. As known for a long time, at zero order in α′ (the string fundamental constant) the first action is pure Yang-Mills while the second one is pure Einstein-Hilbert. The first Superstring Theory corrections turn up to appear at [Formula: see text] order in the first case while they appear at [Formula: see text] in the second one, as known from the three and four-point scattering amplitudes for gluons and gravitons, respectively. Recent work involving the [Formula: see text] order contributions to the Yang-Mills action is reviewed with some detail, including the authors' present line of research. Also, the uncharted territory of five graviton scattering is commented, looking forward to derive the [Formula: see text] Superstring Theory corrections to the Einstein-Hilbert action.

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 The Grassmannian for celestial superamplitudes

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Livia Ferro ◽  
Robert Moerman
Keyword(s):  
Scattering Amplitudes ◽  
Correlation Functions ◽  
Minkowski Spacetime ◽  
Tree Level ◽  
Two Dimensional ◽  
Yang Mills ◽  
Celestial Sphere ◽  
Geometric Picture ◽  
Super Yang Mills Theory ◽  
The Way

Abstract Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries.

scholarly journals Expansions of tree amplitudes for Einstein–Maxwell and other theories

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Kang Zhou ◽  
Shi-Qian Hu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Recent Work ◽  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Quantum Field ◽  
Yang Mills

Abstract The expansions of tree-level scattering amplitudes for one theory into amplitudes for another theory, which have been studied in recent work, exhibit hidden connections between different theories that are invisible in the traditional Lagrangian formulism of quantum field theory. In this paper, the general expansion of tree Einstein–Maxwell amplitudes into the Kleiss–Kuijf basis of tree Yang–Mills amplitudes has been derived by applying a method based on differential operators. The obtained coefficients are shared by the expansion of tree $\phi^4$ amplitudes into tree BS (bi-adjoint scalar) amplitudes and the expansion of tree special Yang–Mills scalar amplitudes into tree BS amplitudes, as well the expansion of tree Dirac–Born–Infeld amplitudes into tree non-linear sigma model amplitudes.

scholarly journals MHV gluon scattering amplitudes from celestial current algebras

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Shamik Banerjee ◽  
Sudip Ghosh
Keyword(s):  
Scattering Amplitudes ◽  
Current Algebra ◽  
Mellin Transform ◽  
Scattering Amplitude ◽  
Correction Term ◽  
Tree Level ◽  
Yang Mills ◽  
First Order ◽  
Leading Term ◽  
Celestial Sphere

Abstract We show that the Mellin transform of an n-point tree level MHV gluon scattering amplitude, also known as the celestial amplitude in pure Yang-Mills theory, satisfies a system of (n−2) linear first order partial differential equations corresponding to (n−2) positive helicity gluons. Although these equations closely resemble Knizhnik-Zamoldochikov equations for SU(N) current algebra there is also an additional “correction” term coming from the subleading soft gluon current algebra. These equations can be used to compute the leading term in the gluon-gluon OPE on the celestial sphere. Similar equations can also be written down for the momentum space tree level MHV scattering amplitudes. We also propose a way to deal with the non closure of subleading current algebra generators under commutation. This is then used to compute some subleading terms in the mixed helicity gluon OPE.

scholarly journals Algebraic singularities of scattering amplitudes from tropical geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Scattering Amplitudes ◽  
Natural Language ◽  
Tropical Geometry ◽  
Cluster Algebras ◽  
Finite Alphabet ◽  
Square Root ◽  
Finite Sets ◽  
Yang Mills ◽  
Square Roots ◽  
Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

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