280 research outputs found
A Grassmannian Etude in NMHV Minors
Arkani-Hamed, Cachazo, Cheung and Kaplan have proposed a Grassmannian
formulation for the S-matrix of N=4 Yang-Mills as an integral over link
variables. In parallel work, the connected prescription for computing tree
amplitudes in Witten's twistor string theory has also been written in terms of
link variables. In this paper we extend the six- and seven-point results of
arXiv:0909.0229 and arXiv:0909.0499 by providing a simple analytic proof of the
equivalence between the two formulas for all tree-level NMHV superamplitudes.
Also we note that a simple deformation of the connected prescription integrand
gives directly the ACCK Grassmannian integrand in the limit when the
deformation parameters equal zero.Comment: 17 page
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
Clinoform architecture and along-strike variability through an exhumed erosional to accretionary basin margin transition
Exhumed basin marginâscale clinothems provide important archives for understanding process interactions and reconstructing the physiography of sedimentary basins. However, studies of coeval shelf through slope to basinâfloor deposits are rarely documented, mainly due to outcrop or subsurface dataset limitations. Unit G from the Laingsburg depocentre (Karoo Basin, South Africa) is a rare example of a complete basin margin scale clinothem (>60 km long, 200 mâhigh), with >10 km of depositional strike control, which allows a quasiâ3D study of a preserved shelfâslopeâbasin floor transition over a ca. 1200 km2 area. Sandâprone, waveâinfluenced topset deposits close to the shelfâedge rollover zone can be physically mapped down dip for ca. 10 km as they thicken and transition into heterolithic foreset/slope deposits. These deposits progressively fine and thin over 10s of km farther down dip into sandâstarved bottomset/basin floor deposits. Only a few km along strike, the coeval foreset/slope deposits are bypassâdominated with incisional features interpreted as minor slope conduits/gullies. The margin here is steeper, more channelized, and records a stepped profile with evidence of sandâfilled intraslope topography, a preserved baseâofâslope transition zone and sandârich bottomset/basinâfloor deposits. Unit G is interpreted as part of a composite depositional sequence that records a change in basin margin style from an underlying incised slope with large sandârich basinâfloor fans to an overlying accretionâdominated shelf with limited sand supply to slope and basinâfloor. The change in margin style is accompanied with decreased clinoform height/slope and increased shelf width. This is interpreted to reflect a transition in subsidence style from regional sag, driven by dynamic topography/inherited basement configuration, to early foreland basin flexural loading. Results of this study caution against reconstructing basin margin successions from partial datasets without accounting for temporal and spatial physiographic changes, with potential implications on predictive basin evolution models
On the Classification of Residues of the Grassmannian
We study leading singularities of scattering amplitudes which are obtained as
residues of an integral over a Grassmannian manifold. We recursively do the
transformation from twistors to momentum twistors and obtain an iterative
formula for Yangian invariants that involves a succession of dualized twistor
variables. This turns out to be useful in addressing the problem of classifying
the residues of the Grassmannian. The iterative formula leads naturally to new
coordinates on the Grassmannian in terms of which both composite and
non-composite residues appear on an equal footing. We write down residue
theorems in these new variables and classify the independent residues for some
simple examples. These variables also explicitly exhibit the distinct solutions
one expects to find for a given set of vanishing minors from Schubert calculus.Comment: 20 page
Multiplicative slices, relativistic Toda and shifted quantum affine algebras
We introduce the shifted quantum affine algebras. They map homomorphically
into the quantized -theoretic Coulomb branches of SUSY
quiver gauge theories. In type , they are endowed with a coproduct, and they
act on the equivariant -theory of parabolic Laumon spaces. In type ,
they are closely related to the open relativistic quantum Toda lattice of type
.Comment: 125 pages. v2: references updated; in section 11 the third local Lax
matrix is introduced. v3: references updated. v4=v5: 131 pages, minor
corrections, table of contents added, Conjecture 10.25 is now replaced by
Theorem 10.25 (whose proof is based on the shuffle approach and is presented
in a new Appendix). v6: Final version as published, references updated,
footnote 4 adde
Some analytic results for two-loop scattering amplitudes
We present analytic results for the finite diagrams contributing to the
two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a
recently proposed representation for the integrand of the amplitude in terms of
(momentum) twistors and focus on a restricted kinematics in which the answer
depends only on two independent cross-ratios. The theory of motives can be used
to vastly simplify the results, which can be expressed as simple combinations
of classical polylogarithms.Comment: 18 page
Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
An on-shell formalism for the computation of S-matrices of SYM theories in
three spacetime dimensions is presented. The framework is a generalization of
the spinor-helicity formalism in four dimensions. The formalism is applied to
establish the manifest SO(N) covariance of the on-shell superalgebra relevant
to N =2,4 and 8 SYM theories in d=3. The results are then used to argue for the
SO(N) invariance of the S-matrices of these theories: a claim which is proved
explicitly for the four-particle scattering amplitudes. Recursion relations
relating tree amplitudes of three-dimensional SYM theories are shown to follow
from their four-dimensional counterparts. The results for the four-particle
amplitudes are verified by tree-level perturbative computations and a unitarity
based construction of the integrand corresponding to the leading perturbative
correction is also presented for the N=8 theory. For N=8 SYM, the manifest
SO(8) symmetry is used to develop a map between the color-ordered amplitudes of
the SYM and superconformal Chern-Simons theories, providing a direct connection
between on-shell observables of D2 and M2-brane theories.Comment: 28 page
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