135 research outputs found
Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
We compute the coefficient of the potential three-loop divergence in pure N=4
supergravity and show that it vanishes, contrary to expectations from symmetry
arguments. The recently uncovered duality between color and kinematics is used
to greatly streamline the calculation. We comment on all-loop cancellations
hinting at further surprises awaiting discovery at higher loops.Comment: 5 pages, 3 figures; v2 added references and minor correction
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
A Twistor Description of Six-Dimensional N=(1,1) Super Yang-Mills Theory
We present a twistor space that describes super null-lines on six-dimensional
N=(1,1) superspace. We then show that there is a one-to-one correspondence
between holomorphic vector bundles over this twistor space and solutions to the
field equations of N=(1,1) super Yang-Mills theory. Our constructions naturally
reduce to those of the twistorial description of maximally supersymmetric
Yang-Mills theory in four dimensions.Comment: 15 pages, typos fixed, published versio
Simple superamplitudes in higher dimensions
We provide simple superspaces based on a formulation of spinor helicity in
general even dimensions. As a distinguishing feature these spaces admit a
fermionic super-momentum conserving delta function solution to the on-shell
supersymmetry Ward identities. Using these solutions, we present beautifully
simple formulae for the complete three, four and five point superamplitudes in
maximal super Yang-Mills theory in eight dimensions, and for the three and four
point superamplitudes in ten dimensional type IIB supergravity. In addition, we
discuss the exceptional kinematics of the three point amplitude, and the
supersymmetric spinorial BCFW recursion, in general dimensions.Comment: 34 page
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
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
We provide an analytic formula for the (rescaled) one-loop scalar hexagon
integral with all external legs massless, in terms of classical
polylogarithms. We show that this integral is closely connected to two
integrals appearing in one- and two-loop amplitudes in planar
super-Yang-Mills theory, and . The derivative of
with respect to one of the conformal invariants yields
, while another first-order differential operator applied to
yields . We also introduce some kinematic
variables that rationalize the arguments of the polylogarithms, making it easy
to verify the latter differential equation. We also give a further example of a
six-dimensional integral relevant for amplitudes in
super-Yang-Mills.Comment: 18 pages, 2 figure
Willing suspension of disbelief: a study in online learning through simulation, and its potential for deeper learning in Higher Education
This article describes the replacement of a 'traditionally taught' law of probate course (lectures and workshops/tutorials) with an on-line collaborative learning exercise using simulation and role-play which is referred to hereafter as the Transactional Learning Project ('TLP'). The article considers the theory that the emotional engagement that comes about through role play in simulation leads to deeper learning, a process Maharg (2010) has dubbed as the 'integration of the cognitive and the affective'. The article includes statistical analysis of student feedback on the TLP in an attempt to measure how easy it is to carry students predisposed to expect information to be 'given' rather than 'acquired' along the journey leading away from traditional didactic teaching. The project was motivated partly by the dearth of such learning practices on the Legal Practice Course. It is suggested that the findings of the project add to the body of research which tends to illustrate the success in terms of student learning from working in leaderless (i.e. where the tutor is absent from the collaborative group) groups engaged in practical tasks involving simulation
Yangian symmetry of light-like Wilson loops
We show that a certain class of light-like Wilson loops exhibits a Yangian
symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops
we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills
theory in a certain kinematical regime. The fact that we find a Yangian
symmetry constraining their functional form can be thought of as the effect of
the original conformal symmetry associated to the scattering amplitudes in the
N=4 theory.Comment: 15 pages, 5 figure
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