Yangians, Grassmannians and T-duality

Abstract

We investigate the Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out. The equivalence of this picture with the one where the ordinary superconformal symmetry is thought of as fundamental is an algebraic expression of T-duality. Motivated by this, we analyse some recently proposed formulas, which reproduce different contributions to amplitudes through a Grassmannian integral. We prove their Yangian invariance by directly applying the generators.

28 pages, 1 figure; v2: minor corrections

References in corpus (20)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• All tree-level amplitudes in N=4 SYM
• Unification of Residues and Grassmannian Dualities
• Exacting N=4 Superconformal Symmetry
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Twistor-Strings, Grassmannians and Leading Singularities
• Eliminating spurious poles from gauge-theoretic amplitudes
• Unraveling L_{n,k}: Grassmannian Kinematics
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Symmetries of the N=4 SYM S-matrix

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• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
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• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• Superconformal invariants for scattering amplitudes in N=4 SYM theory
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
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• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
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• Getting more flavour out of one-flavour QCD
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• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
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• Cluster Adjacency for m=2 Yangian Invariants
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• Null Polygonal Wilson Loops in Full N=4 Superspace
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• Scattering Amplitudes and Toric Geometry
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• Hidden Simplicity of Gauge Theory Amplitudes
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
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• On the Classification of Residues of the Grassmannian
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• Yangian in the Twistor String
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Yangian Symmetry in N=4 super Yang-Mills
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Yangian symmetry of light-like Wilson loops
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• Weak Separation, Positivity and Extremal Yangian Invariants
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes
• A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes