A super MHV vertex expansion for N=4 SYM theory

Abstract

We present a supersymmetric generalization of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory. In addition to the choice of a reference spinor, this super MHV vertex expansion also depends on four reference Grassmann parameters. We demonstrate that a significant fraction of diagrams in the expansion vanishes for a judicious choice of these Grassmann parameters, which simplifies the computation of amplitudes. Even pure-gluon amplitudes require fewer diagrams than in the ordinary MHV vertex expansion. We show that the super MHV vertex expansion arises from the recursion relation associated with a holomorphic all-line supershift. This is a supersymmetric generalization of the holomorphic all-line shift recently introduced in arXiv:0811.3624. We study the large-z behavior of generating functions under these all-line supershifts, and find that they generically provide 1/z^k falloff at (Next-to)^k MHV level. In the case of anti-MHV generating functions, we find that a careful choice of shift parameters guarantees a stronger 1/z^(k+4) falloff. These particular all-line supershifts may therefore play an important role in extending the super MHV vertex expansion to N=8 supergravity.

26 pages, 3 figures, v2: analytic expression for counting of super MHV vertex diagrams added; references added

References in corpus (65)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• What is the Simplest Quantum Field Theory?
• Magic identities for conformal four-point integrals
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Comments on gluon scattering amplitudes via AdS/CFT
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Direct extraction of one-loop integral coefficients
• On Tree Amplitudes in Gauge Theory and Gravity
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Three-Loop Superfiniteness of N=8 Supergravity
• On the Tree-Level S-Matrix of Yang-Mills Theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• A direct proof of the CSW rules
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• All tree-level amplitudes in N=4 SYM
• Ultraviolet properties of Maximal Supergravity
• Taming Tree Amplitudes In General Relativity
• Non-MHV Tree Amplitudes in Gauge Theory
• Supersymmetric Gauge Theories in Twistor Space
• Unexpected Cancellations in Gravity Theories
• From Twistor Actions to MHV Diagrams
• Generalized unitarity for N=4 super-amplitudes
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• The No-Triangle Hypothesis for N=8 Supergravity
• On-Shell Recursion Relations for Generic Theories
• Gravity, Twistors and the MHV Formalism
• MHV-Vertices for Gravity Amplitudes
• On T-Duality and Integrability for Strings on AdS Backgrounds
• The Lagrangian origin of MHV rules
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Absence of Triangles in Maximal Supergravity Amplitudes
• KLT relations from the Einstein-Hilbert Lagrangian
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• From Yang-Mills Lagrangian to MHV Diagrams
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Note on graviton MHV amplitudes
• Tree-Level Amplitudes in N=8 Supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Three Applications of a Bonus Relation for Gravity Amplitudes
• One-loop MHV Rules and Pure Yang-Mills
• Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• Amplitudes in Pure Yang-Mills and MHV Diagrams
• Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
• QCD recursion relations from the largest time equation
• Planar scattering amplitudes from Wilson loops
• MHV Lagrangian for N=4 Super Yang-Mills
• Progress on Ultraviolet Finiteness of Supergravity

Cited by in corpus (15)

• Gravity as the Square of Gauge Theory
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Basics of Generalized Unitarity
• On-shell constructibility of tree amplitudes in general field theories
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Solution to the Ward Identities for Superamplitudes
• Massive amplitudes on the Coulomb branch of N=4 SYM
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• On-shell superamplitudes in N<4 SYM
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• The Coulomb-branch S-matrix from massless amplitudes
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop