95 research outputs found
Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory.
The proof uses a shift acting on all external momenta, and we show that every
N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this
shift. The MHV vertex expansion allows us to derive compact and efficient
generating functions for all N^kMHV tree amplitudes of the theory. We also
derive an improved form of the anti-NMHV generating function. The proof leads
to a curious set of sum rules for the diagrams of the MHV vertex expansion.Comment: 40 pages, 7 figure
Multigluon tree amplitudes with a pair of massive fermions
We consider the calculation of n-point multigluon tree amplitudes with a pair
of massive fermions in QCD. We give the explicit transformation rules of this
kind of massive fermion-pair amplitudes with respect to different reference
momenta and check the correctness of them by SUSY Ward identities. Using these
rules and onshell BCFW recursion relation, we calculate the analytic results of
several n-point multigluon amplitudes.Comment: 15page
A super MHV vertex expansion for N=4 SYM theory
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.Comment: 26 pages, 3 figures, v2: analytic expression for counting of super
MHV vertex diagrams added; references adde
Identification of animal movement patterns using tri-axial magnetometry
BackgroundAccelerometers are powerful sensors in many bio-logging devices, and are increasingly allowing researchers to investigate the performance, behaviour, energy expenditure and even state, of free-living animals. Another sensor commonly used in animal-attached loggers is the magnetometer, which has been primarily used in dead-reckoning or inertial measurement tags, but little outside that. We examine the potential of magnetometers for helping elucidate the behaviour of animals in a manner analogous to, but very different from, accelerometers. The particular responses of magnetometers to movement means that there are instances when they can resolve behaviours that are not easily perceived using accelerometers.MethodsWe calibrated the tri-axial magnetometer to rotations in each axis of movement and constructed 3-dimensional plots to inspect these stylised movements. Using the tri-axial data of Daily Diary tags, attached to individuals of number of animal species as they perform different behaviours, we used these 3-d plots to develop a framework with which tri-axial magnetometry data can be examined and introduce metrics that should help quantify movement and behaviour.ResultsTri-axial magnetometry data reveal patterns in movement at various scales of rotation that are not always evident in acceleration data. Some of these patterns may be obscure until visualised in 3D space as tri-axial spherical plots (m-spheres). A tag-fitted animal that rotates in heading while adopting a constant body attitude produces a ring of data around the pole of the m-sphere that we define as its Normal Operational Plane (NOP). Data that do not lie on this ring are created by postural rotations of the animal as it pitches and/or rolls. Consequently, stereotyped behaviours appear as specific trajectories on the sphere (m-prints), reflecting conserved sequences of postural changes (and/or angular velocities), which result from the precise relationship between body attitude and heading. This novel approach shows promise for helping researchers to identify and quantify behaviours in terms of animal body posture, including heading.ConclusionMagnetometer-based techniques and metrics can enhance our capacity to identify and examine animal behaviour, either as a technique used alone, or one that is complementary to tri-axial accelerometry
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 amplitudes by examining the amplitudes in
momentum space. In this paper, we construct the actual twistor scattering
amplitudes themselves. We show that the recursion relations of Britto, Cachazo,
Feng and Witten have a natural twistor formulation that, together with the
three-point seed amplitudes, allows us to recursively construct general tree
amplitudes in twistor space. We obtain explicit formulae for -particle MHV
and NMHV super-amplitudes, their CPT conjugates (whose representations are
distinct in our chiral framework), and the eight particle N^2MHV
super-amplitude. We also give simple closed form formulae for the N=8
supergravity recursion and the MHV and conjugate MHV amplitudes. This gives a
formulation of scattering amplitudes in maximally supersymmetric theories in
which superconformal symmetry and its breaking is manifest. For N^kMHV, the
amplitudes are given by 2n-4 integrals in the form of Hilbert transforms of a
product of purely geometric, superconformally invariant twistor delta
functions, dressed by certain sign operators. These sign operators subtly
violate conformal invariance, even for tree-level amplitudes in N=4 super
Yang-Mills, and we trace their origin to a topological property of split
signature space-time. We develop the twistor transform to relate our work to
the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed,
Cachazo, Cheung and Kaplan.Comment: v2: minor corrections + extra refs. v3: further minor corrections,
extra discussion of signature issues + more ref
Use of bio-loggers to characterize red fox behavior with implications for studies of magnetic alignment responses in free-roaming animals
Glucose increases hepatic lipase expression in HepG2 liver cells through upregulation of upstream stimulatory factors 1 and 2
Path segmentation for beginners: an overview of current methods for detecting changes in animal movement patterns
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