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Direct proof of the tree-level scattering amplitude recursion relation in Yang-mills theory.
Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give aExpand
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New recursion relations for tree amplitudes of gluons
Abstract We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products ofExpand
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MHV vertices and tree amplitudes in gauge theory
As an alternative to the usual Feynman graphs, tree amplitudes in Yang-Mills theory can be constructed from tree graphs in which the vertices are tree level MHV scattering amplitudes, continued offExpand
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Scattering of massless particles in arbitrary dimensions.
We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions. The new formula for the scattering of n particles is givenExpand
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A Geometric unification of dualities
Abstract We study the dynamics of a large class of N =1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi–Yau three-folds. These include N =2 (affine)Expand
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What is the simplest quantum field theory?
Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however beenExpand
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Chiral Rings and Anomalies in Supersymmetric Gauge Theory
Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitraryExpand
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A duality for the S matrix
We propose a dual formulation for the S Matrix of $$ \mathcal N $$ = 4 SYM. The dual provides a basis for the “leading singularities” of scattering amplitudes to all orders in perturbation theory,Expand
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A large N duality via a geometric transition
Abstract We propose a large N dual of 4d, N =1 supersymmetric, SU ( N ) Yang–Mills with adjoint field Φ and arbitrary superpotential W ( Φ ). The field theory is geometrically engineered via D-branesExpand
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Scattering Amplitudes and the Positive Grassmannian
We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physicalExpand
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