444 research outputs found
Consistency Conditions on S-Matrix of Spin 1 Massless Particles
Motivated by new techniques in the computation of scattering amplitudes of
massless particles in four dimensions, like BCFW recursion relations, the
question of how much structure of the S-matrix can be determined from purely
S-matrix arguments has received new attention. The BCFW recursion relations for
massless particles of spin 1 and 2 imply that the whole tree-level S-matrix can
be determined in terms of three-particle amplitudes (evaluated at complex
momenta). However, the known proofs of the validity of the relations rely on
the Lagrangian of the theory, either by using Feynman diagrams explicitly or by
studying the effective theory at large complex momenta. This means that a
purely S-matrix theoretic proof of the relations is still missing. The aim of
this paper is to provide such a proof for spin 1 particles by extending the
four-particle test introduced by P. Benincasa and F. Cachazo in
arXiv:0705.4305[hep-th] to all particles. We show how n-particle tests imply
that the rational function built from the BCFW recursion relations possesses
all the correct factorization channels including holomorphic and
anti-holomorphic collinear limits. This in turn implies that they give the
correct S-matrix of the theory.Comment: 24 pages, 4 figure
The Yangian origin of the Grassmannian integral
In this paper we analyse formulas which reproduce different contributions to
scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian
integral. Recently their Yangian invariance has been proved directly by using
the explicit expression of the Yangian level-one generators. The specific
cyclic structure of the form integrated over the Grassmannian enters in a
crucial way in demonstrating the symmetry. Here we show that the Yangian
symmetry fixes this structure uniquely.Comment: 26 pages. v2: typos corrected, published versio
From lightcone actions to maximally supersymmetric amplitudes
In this article actions for N=4 SYM and N=8 supergravity are formulated in
terms of a chiral superfield, which contains only the physical degrees of
freedom of either theory. In these new actions, which originate from the
lightcone superspace, the supergravity cubic vertex is the square of the gauge
theory one (omitting the color structures). Amplitude calculations using the
corresponding Feynman supergraph rules are tedious, but can be simplified by
choosing a preferred superframe. Recursive calculations of all MHV amplitudes
in N=4 SYM and the four-point N=8 supergravity amplitude are shown to agree
with the known results and connections to the BCFW recursion relations are
pointed out. Finally, the new path integrals are discussed in the context of
the double-copy property relating N=4 SYM theory to N=8 supergravity.Comment: 29 pages, 2 figures, v2: title modified, published versio
Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
Infrared equations and dual conformal constraints arise as consistency
conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions
are linear relations between leading singularities, which can be computed in
the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently.
Examples for infrared equations have been shown to be implied by global residue
theorems in the Grassmannian picture. Both dual conformal constraints and
infrared equations are mapped explicitly to global residue theorems for
one-loop next-to-maximally-helicity-violating amplitudes. In addition, the
identity relating the BCFW and its parity-conjugated form of tree-level
amplitudes, is shown to emerge from a particular combination of global residue
theorems.Comment: 21 page
A note on the boundary contribution with bad deformation in gauge theory
Motivated by recently progresses in the study of BCFW recursion relation with
nonzero boundary contributions for theories with scalars and
fermions\cite{Bofeng}, in this short note we continue the study of boundary
contributions of gauge theory with the bad deformation. Unlike cases with
scalars or fermions, it is hard to use Feynman diagrams directly to obtain
boundary contributions, thus we propose another method based on the SYM theory. Using this method, we are able to write down a useful
on-shell recursion relation to calculate boundary contributions from related
theories. Our result shows the cut-constructibility of gauge theory even with
the bad deformation in some generalized sense.Comment: 16 pages, 7 figure
The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
We present a new, explicit formula for all tree-level amplitudes in N=4 super
Yang-Mills. The formula is written as a certain contour integral of the
connected prescription of Witten's twistor string, expressed in link variables.
A very simple deformation of the integrand gives directly the Grassmannian
integrand proposed by Arkani-Hamed et al. together with the explicit contour of
integration. The integral is derived by iteratively adding particles to the
Grassmannian integral, one particle at a time, and makes manifest both parity
and soft limits. The formula is shown to be related to those given by Dolan and
Goddard, and generalizes the results of earlier work for NMHV and N^2MHV to all
N^(k-2)MHV tree amplitudes in N=4 super Yang-Mills.Comment: 26 page
On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
We study the relationship between the momentum twistor MHV vertex expansion
of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of
the BCFW recursion relations. We demonstrate explicitly in several examples
that the MHV vertex expressions for tree-level amplitudes and loop integrands
satisfy the recursion relations. Furthermore, we introduce a rewriting of the
MHV expansion in terms of sums over non-crossing partitions and show that this
cyclically invariant formula satisfies the recursion relations for all numbers
of legs and all loop orders.Comment: 34 pages, 17 figures; v2: Minor improvements to exposition and
discussion, updated references, typos fixe
Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills
theory in six dimensions, when stripped of their overall momentum and
supermomentum delta functions, are covariant with respect to the
six-dimensional dual conformal group. Using the generalized unitarity method,
we demonstrate that this property is also present for loop amplitudes. Since
the six-dimensional amplitudes can be interpreted as massive four-dimensional
ones, this implies that the six-dimensional symmetry is also present in the
massively regulated four-dimensional maximal super-Yang-Mills amplitudes.Comment: 20 pages, 3 figures, minor clarification, references update
No triangles on the moduli space of maximally supersymmetric gauge theory
Maximally supersymmetric gauge theory in four dimensions has a remarkably
simple S-matrix at the origin of its moduli space at both tree and loop level.
This leads to the question what, if any, of this structure survives at the
complement of this one point. Here this question is studied in detail at one
loop for the branch of the moduli space parameterized by a vacuum expectation
value for one complex scalar. Motivated by the parallel D-brane picture of
spontaneous symmetry breaking a simple relation is demonstrated between the
Lagrangian of broken super Yang-Mills theory and that of its higher dimensional
unbroken cousin. Using this relation it is proven both through an on- as well
as an off-shell method there are no so-called triangle coefficients in the
natural basis of one-loop functions at any finite point of the moduli space for
the theory under study. The off-shell method yields in addition absence of
rational terms in a class of theories on the Coulomb branch which includes the
special case of maximal supersymmetry. The results in this article provide
direct field theory evidence for a recently proposed exact dual conformal
symmetry motivated by the AdS/CFT correspondence.Comment: 39 pages, 4 figure
Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
The spinor helicity formalism in four dimensions has become a very useful
tool both for understanding the structure of amplitudes and also for practical
numerical computation of amplitudes. Recently, there has been some discussion
of an extension of this formalism to higher dimensions. We describe a
particular implementation of the spinor-helicity method in ten dimensions.
Using this tool, we study the tree-level S-matrix of ten dimensional super
Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry.
Implications for four-dimensional computations are discussed.Comment: 24 pages, 1 figure
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