Grassmannians and form factors with $q^2=0$ in N=4 SYM theory

Abstract

We consider tree level form factors of operators from stress tensor operator supermultiplet with light-like operator momentum $q^2=0$. We present a conjecture for the Grassmannian integral representation both for these tree level form factors as well as for leading singularities of their loop counterparts. The presented conjecture was successfully checked by reproducing several known answers in $\mbox{MHV}$ and $\mbox{N}^{k-2}\mbox{MHV}$, $k\ge 3$ sectors together with appropriate soft limits. We also discuss the cancellation of spurious poles and relations between different BCFW representations for such form factors on simple examples.

arXiv comment46 pages, 16 figures; v2: minor changes, typos corrected, references added

References in corpus (52)

• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• The Amplituhedron
• A Duality For The S Matrix
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Progress in One-Loop QCD Computations
• On-Shell Methods in Perturbative QCD
• Into the Amplituhedron
• Form factors at strong coupling via a Y-system
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Unification of Residues and Grassmannian Dualities
• The super-correlator/super-amplitude duality: Part I
• Color-kinematic Duality for Form Factors
• Analytic two-loop form factors in N=4 SYM
• (N,p,q) Harmonic Superspace
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Harmony of Super Form Factors
• Yangians, Grassmannians and T-duality
• The Yangian origin of the Grassmannian integral
• Evidence for a Nonplanar Amplituhedron
• On form factors in N=4 sym
• The three-loop form factor in N=4 super Yang-Mills
• A Note on Polytopes for Scattering Amplitudes
• Bipartite Field Theories: from D-Brane Probes to Scattering Amplitudes
• The last of the simple remainders
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• On super form factors of half-BPS operators in N=4 super Yang-Mills
• The Amplituhedron from Momentum Twistor Diagrams
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• Towards the Amplituhedron Volume
• On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Master integrals for the four-loop Sudakov form factor
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• On Form Factors in N=4 SYM Theory and Polytopes
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• On tree form-factors in (supersymmetric) Yang-Mills theory
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• A dictionary between R-operators, on-shell graphs and Yangian algebras
• Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
• Two-loop Sudakov Form Factor in ABJM
• Form Factors of Chiral Primary Operators at Two Loops in ABJ(M)
• Form Factor and Boundary Contribution of Amplitude
• ABJM amplitudes and WL at finite N
• Soft Theorem of N=4 SYM in Grassmannian Formulation

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• A Three-Point Form Factor Through Five Loops
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Dual conformal invariance for form factors
• Full-color three-loop three-point form factors in N=4 SYM
• On Form Factors and Correlation Functions in Twistor Space
• Form factor recursion relations at loop level
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• The all-loop conjecture for integrands of reggeon amplitudes in N=4 SYM
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Form factors from string amplitudes
• A note on NMHV form factors from the Graßmannian and the twistor string
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM