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 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 Bootstrapping octagons in reduced kinematics from A2 cluster algebras

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Yichao Tang ◽  
Qinglin Yang
Keyword(s):  
Scattering Amplitudes ◽  
Minkowski Spacetime ◽  
Dimensional Subspace ◽  
Cluster Algebras ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Feynman Integrals ◽  
Yang Mills ◽  
Two Sectors ◽  
Special Case

Abstract Multi-loop scattering amplitudes/null polygonal Wilson loops in $$ \mathcal{N} $$ N = 4 super-Yang-Mills are known to simplify significantly in reduced kinematics, where external legs/edges lie in an 1 + 1 dimensional subspace of Minkowski spacetime (or boundary of the AdS3 subspace). Since the edges of a 2n-gon with even and odd labels go along two different null directions, the kinematics is reduced to two copies of G(2, n)/T ∼ An−3. In the simplest octagon case, we conjecture that all loop amplitudes and Feynman integrals are given in terms of two overlapping A2 functions (a special case of two-dimensional harmonic polylogarithms): in addition to the letters v, 1 + v, w, 1 + w of A1 × A1, there are two letters v − w, 1 − vw mixing the two sectors but they never appear together in the same term; these are the reduced version of four-mass-box algebraic letters. Evidence supporting our conjecture includes all known octagon amplitudes as well as new computations of multi-loop integrals in reduced kinematics. By leveraging this alphabet and conditions on first and last entries, we initiate a bootstrap program in reduced kinematics: within the remarkably simple space of overlapping A2 functions, we easily obtain octagon amplitudes up to two-loop NMHV and three-loop MHV. We also briefly comment on the generalization to 2n-gons in terms of A2 functions and beyond.

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 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 Spectral parameters for scattering amplitudes in $ \mathcal{N} $ =4 super Yang-Mills theory

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Livia Ferro ◽  
Tomasz Lukowski ◽  
Carlo Meneghelli ◽  
Jan Plefka ◽  
Matthias Staudacher
Keyword(s):  
Scattering Amplitudes ◽  
Spectral Parameters ◽  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals Yangian symmetry of scattering amplitudes in 𝒩 = 4 super Yang-Mills theory

2009 ◽  
Vol 2009 (05) ◽  
pp. 046-046 ◽  
Author(s):  
James Drummond ◽  
Johannes Henn ◽  
Jan Plefka
Keyword(s):  
Scattering Amplitudes ◽  
Yang Mills ◽  
Yangian Symmetry ◽  
Super Yang Mills 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.

CORRELATION FUNCTIONS AND ZERO MODES ON HIGHER GENUS RIEMANN SURFACES

1988 ◽  
Vol 03 (04) ◽  
pp. 841-860 ◽  
Author(s):  
M. BONINI ◽  
R. IENGO
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Covariant Formulation ◽  
Two Dimensional ◽  
Zero Modes ◽  
Modular Transformation ◽  
Higher Genus

We describe systematically the propagators and the zero modes of the various two dimensional fields which appear in the construction of the scattering amplitudes in the string theory, within the framework of the covariant formulation, and we discuss also their modular transformation properties.

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