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 MHV graviton scattering amplitudes and current algebra on the celestial sphere

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Shamik Banerjee ◽  
Sudip Ghosh ◽  
Partha Paul
Keyword(s):  
Scattering Amplitudes ◽  
Differential Equations ◽  
Current Algebra ◽  
Minimal Model ◽  
Symmetry Algebra ◽  
Local Symmetry ◽  
The Other ◽  
System Of Differential Equations ◽  
First Order ◽  
Celestial Sphere

Abstract The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ currents. This naturally gives rise to a $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ current algebra living on the celestial sphere. The generators of the $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have null states under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An n point MHV amplitude satisfies two systems of (n − 2) linear first order PDEs corresponding to (n − 2) positive helicity gravitons. We have checked, using Hodges’ formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations.This points to the existence of an autonomous sector of the Celestial CFT which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of 2-D CFT.

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 Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

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.

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 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 Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Shamik Banerjee ◽  
Sudip Ghosh ◽  
Sai Satyam Samal
Keyword(s):  
Scattering Amplitudes ◽  
Current Algebra ◽  
Tree Level

Abstract In [8] it was shown that supertranslation and $$ \overline{\mathrm{SL}\left(2,\mathbb{C}\right)} $$ SL 2 ℂ ¯ current algebra symmetries, corresponding to leading and subleading soft graviton theorems, are enough to determine the tree level MHV graviton scattering amplitudes. In this note we clarify the role of subsubleading soft graviton theorem in this context.

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.

scholarly journals Celestial operator products of gluons and gravitons

2021 ◽  
pp. 2140003
Author(s):  
Monica Pate ◽  
Ana-Maria Raclariu ◽  
Andrew Strominger ◽  
Ellis Ye Yuan
Keyword(s):  
Operator Product Expansion ◽  
Beta Function ◽  
Tree Level ◽  
Operator Product ◽  
Recursion Relations ◽  
Yang Mills ◽  
Euler Beta Function ◽  
Celestial Sphere ◽  
Asymptotic Symmetries

The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein–Yang–Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.

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