From twistor string theory to recursion relations

  title={From twistor string theory to recursion relations},
  author={Marcus Spradlin and Anastasia Volovich},
  journal={Physical Review D},
Witten's twistor string theory gives rise to an enigmatic formula [1] known as the ``connected prescription'' for tree-level Yang-Mills scattering amplitudes. We derive a link representation for the connected prescription by Fourier transforming it to mixed coordinates in terms of both twistor and dual twistor variables. We show that it can be related to other representations of amplitudes by applying the global residue theorem to deform the contour of integration. For six and seven particles… 

The Grassmannian and the twistor string: connecting all trees in $ \mathcal{N} = 4 $ SYM

We present a new, explicit formula for all tree-level amplitudes in $ \mathcal{N} = 4 $ super Yang-Mills. The formula is written as a certain contour integral of the connected prescription of

Twistor-strings, Grassmannians and leading singularities

We derive a systematic procedure for obtaining explicit, ℓ-loop leading singularities of planar $$ \mathcal{N} $$ = 4 super Yang-Mills scattering amplitudes in twistor space directly from their

Scattering in three dimensions from rational maps

A bstractThe complete tree-level S-matrix of four dimensional $ \mathcal{N}=4 $ super Yang-Mills and $ \mathcal{N}=8 $ supergravity has compact forms as integrals over the moduli space of certain

The connected prescription for form factors in twistor space

A bstractWe propose a connected prescription formula in twistor space for all tree-level form factors of the stress tensor multiplet operator in N$$ \mathcal{N} $$ = 4 super Yang-Mills, which is a

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM

We give an explicit recursive formula for the all ℓ-loop integrand for scattering amplitudes in $ \mathcal{N} = 4 $ SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This

Local spacetime physics from the Grassmannian

A duality has recently been conjectured between all leading singularities of n-particle Nk−2MHV scattering amplitudes in $ \mathcal{N} = 4 $ SYM and the residues of a contour integral with a natural

Scattering amplitudes and Wilson loops in twistor space

This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for super-Yang–Mills. Wilson loops and amplitudes are derived from first principles using

Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica

We describe an efficient implementation of the BCFW recursion relations for tree-amplitudes in N=4 super Yang-Mills, which can generate analytic formulae for general N^kMHV colour-ordered

Gravity in Twistor Space and its Grassmannian Formulation

We prove the formula for the complete tree-level S-matrix of N = 8 super- gravity recently conjectured by two of the authors. The proof proceeds by showing that the new formula satisfies the same

A link representation for gravity amplitudes

A bstractWe derive a link representation for all tree amplitudes in $ \mathcal{N}=8 $ supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as



The S-matrix in twistor space

The marvelous simplicity and remarkable hidden symmetries recently uncovered in (Super) Yang-Mills and (Super)Gravity scattering amplitudes strongly suggests the existence of a “weak-weak” dual

Scattering amplitudes and BCFW recursion in twistor space

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering

On the tree level S matrix of Yang-Mills theory

In this note we further investigate the procedure for computing tree-level amplitudes in Yang-Mills theory from connected instantons in the B-model on P^{3|4}, emphasizing that the problem of

Equivalence of twistor prescriptions for super Yang-Mills

There is evidence that one can compute tree-level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We give a partial explanation of the

Perturbative Gauge Theory as a String Theory in Twistor Space

Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier

Parity Invariance For String In Twistor Space

Topological string theory with twistor space as the target makes visible some otherwise difficult to see properties of perturbative Yang-Mills theory. But left-right symmetry, which is obvious in the

Parity Invariance For Strings In Twistor Space

Topological string theory with twistor space as the target makes visible some otherwise difficult to see properties of perturbative Yang-Mills theory. But left-right symmetry, which is obvious in the


Tree-level gluon scattering amplitudes in Yang-Mills theory frequently display simple mathematical structure which is completely obscure in the calculation of Feynman diagrams. We describe a novel

Twistor-space recursive formulation of gauge-theory amplitudes

Using twistor-space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define