499 research outputs found
N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
We further investigate, in the planar limit of N=4 supersymmetric Yang Mills
theories,the high energy Regge behavior of six-point MHV scattering amplitudes.
In particular, for the new Regge cut contribution found in our previous paper,
we compute in the leading logarithmic approximation (LLA) the energy spectrum
of the BFKL equation in the color octet channel, and we calculate explicitly
the two loop corrections to the discontinuities of the amplitudes for the
transitions 2 to 4 and 3 to 3. We find an explicit solution of the BFKL
equation for the octet channel for arbitrary momentum transfers and investigate
the intercepts of the Regge singularities in this channel. As an important
result we find that the universal collinear and infrared singularities of the
BDS formula are not affected by this Regge-cut contribution. Any improvement of
the BDS formula should reproduce this cut to all orders in the coupling
A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
We construct super Yang-Mills theories with extended supersymmetry on
hypercubic lattices of various dimensions keeping one or two supercharges
exactly. Gauge fields are represented by ordinary unitary link variables, and
the exact supercharges are nilpotent up to gauge transformations. Among the
models, we show that the desired continuum theories are obtained without any
fine tuning of parameters for the cases in two-dimensions.Comment: 29 pages, 1 figure, LaTeX, (v2) problem on degenerate vacua
discussed, renormalization arguments modified, (v3) explanations and
references added, published version in JHE
Iterated amplitudes in the high-energy limit
We consider the high-energy limits of the colour ordered four-, five- and
six-gluon MHV amplitudes of the maximally supersymmetric QCD in the multi-Regge
kinematics where all the gluons are strongly ordered in rapidity. We show that
various building blocks occurring in the Regge factorisation (the Regge
trajectory, the coefficient functions and the Lipatov vertex) satisfy an
iterative structure very similar to the Bern-Dixon-Smirnov (BDS) ansatz. This
iterative structure, combined with the universality of the building blocks,
enables us to show that in the Euclidean region any two- and three-loop
amplitude in multi-Regge kinematics is guaranteed to satisfy the BDS ansatz. We
also consider slightly more general kinematics where the strong rapidity
ordering applies to all the gluons except the two with either the largest or
smallest rapidities, and we derive the iterative formula for the associated
coefficient function. We show that in this kinematic limit the BDS ansatz is
also satisfied. Finally, we argue that only for more general kinematics - e.g.
with three gluons having similar rapidities, or where the two central gluons
have similar rapidities - can a disagreement with the BDS ansatz arise.Comment: Version corresponding to the Erratum sent to JHEP on October 16th
200
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently
been shown to transform covariantly with respect to a 'dual' superconformal
symmetry algebra, thus extending the conventional superconformal symmetry
algebra psu(2,2|4) of the theory. In this paper we derive the action of the
dual superconformal generators in on-shell superspace and extend the dual
generators suitably to leave scattering amplitudes invariant. We then study the
algebra of standard and dual symmetry generators and show that the inclusion of
the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a
Yangian. The non-local Yangian generators acting on amplitudes turn out to be
cyclically invariant due to special properties of psu(2,2|4). The
representation of the Yangian generators takes the same form as in the case of
local operators, suggesting that the Yangian symmetry is an intrinsic property
of planar N=4 super Yang-Mills, at least at tree level.Comment: 23 pages, no figures; v2: typos corrected, references added; v3:
minor changes, references adde
On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
A closed formula is obtained for the infrared singularities of dimensionally
regularized, massless gauge-theory scattering amplitudes with an arbitrary
number of legs and loops. It follows from an all-order conjecture for the
anomalous-dimension matrix of n-jet operators in soft-collinear effective
theory. We show that the form of this anomalous dimension is severely
constrained by soft-collinear factorization, non-abelian exponentiation, and
the behavior of amplitudes in collinear limits. Using a diagrammatic analysis,
we demonstrate that these constraints imply that to three-loop order the
anomalous dimension involves only two-parton correlations, with the possible
exception of a single color structure multiplying a function of conformal cross
ratios depending on the momenta of four external partons, which would have to
vanish in all two-particle collinear limits. We argue that such a function does
not appear at three-loop order, and that the same is true in higher orders. Our
formula predicts Casimir scaling of the cusp anomalous dimension to all orders
in perturbation theory, and we explicitly check that the constraints exclude
the appearance of higher Casimir invariants at four loops. Using known results
for the quark and gluon form factors, we derive the three-loop coefficients of
the 1/epsilon^n pole terms (with n=1,...,6) for an arbitrary n-parton
scattering amplitude in massless QCD. This generalizes Catani's two-loop
formula proposed in 1998.Comment: 46 pages, 9 figures; v2: improved treatment of collinear limits,
references added; v3: improved discussion of non-abelian exponentiation,
references updated; v4: typo in eq. (17) fixed, references updated; v5:
additional term in (17
Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture
The present study illuminates the relation between null cusped Wilson loops
and their corresponding amplitudes. We find that, compared to the case with no
self-crossing, the one loop expectation value of a self-intersecting Wilson
loop develops an additional 1/\epsilon singularity associated to the
intersection. Interestingly, the same 1/\epsilon pole exists in the finite part
of the one loop amplitude, appearing in the BDS conjecture, at the
corresponding kinematic limit. At two loops, we explore the behaviour of the
remainder function R, encoding the deviation of the amplitude from the BDS
conjecture. By analysing the renormalisation group equations for the Wilson
loop with a simple self-crossing, we argue that, when approaching the
configuration with a self-crossing (u_2 \to 1, u_1\approx u_3), R diverges in
the imaginary direction like R ~ i \pi \log^3(1-u_2). This behaviour can be
attributed to the non-trivial analytic continuation needed when passing from
the Euclidean to the physical region and suggests that R has a branch cut in
the negative u_2 axis when the two other cross ratios are approximately equal
(u_1 \approx u_3).Comment: 23 pages, 1 figure, typos corrected,references adde
Lattice Sigma Models with Exact Supersymmetry
We show how to construct lattice sigma models in one, two and four dimensions
which exhibit an exact fermionic symmetry. These models are discretized and
{\it twisted} versions of conventional supersymmetric sigma models with N=2
supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built
from the original supercharges. The lattice theories possess local actions and
in many cases admit a Wilson term to suppress doubles. In the two and four
dimensional theorie s we show that these lattice theories are invariant under
additional discrete symmetries. We argue that the presence of these exact
symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry
in the continuum limit. As a concrete example we show preliminary numerical
results from a simulation of the O(3) supersymmetric sigma model in two
dimensions.Comment: 23 pages, 3 figures, formalism generalized to allow for explicit
Wilson mass terms. New numerical results added. Version to be published in
JHE
A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
We propose a discretization of two dimensional Euclidean Yang-Mills theories
with N=2 supersymmetry which preserves exactly both gauge invariance and an
element of supersymmetry. The approach starts from the twisted form of the
continuum super Yang Mills action which we show may be written in terms of two
real Kahler-Dirac fields whose components transform into each other under the
twisted supersymmetry. Once the theory is written in this geometrical language
it is straightforward to discretize by mapping the component tensor fields to
appropriate geometrical structures in the lattice and by replacing the
continuum exterior derivative and its adjoint by appropriate lattice covariant
difference operators. The lattice action is local and possesses a unique vacuum
state while the use of Kahler-Dirac fermions ensures the model does not exhibit
spectrum doubling.Comment: Minor typos fixed. Version to be published in JHE
Glauber - Gribov approach for DIS on nuclei in N=4 SYM
In this paper the Glauber-Gribov approach for deep-inelastic scattering (DIS)
with nuclei is developed in N=4 SYM. It is shown that the amplitude displays
the same general properties, such as geometrical scaling, as is the case in the
high density QCD approach. We found that the quantum effects leading to the
graviton reggeization, give rise to an imaginary part of the nucleon amplitude,
which makes the DIS in N=4 SYM almost identical to the one expected in high
density QCD. We concluded that the impact parameter dependence of the nucleon
amplitude is very essential for N=4 SYM, and the entire kinematic region can be
divided into three regions which are discussed in the paper. We revisited the
dipole description for DIS and proposed a new renormalized Lagrangian for the
shock wave formalism which reproduces the Glauber-Gribov approach in a certain
kinematic region. However the saturation momentum turns out to be independent
of energy, as it has been discussed by Albacete, Kovchegov and Taliotis. We
discuss the physical meaning of such a saturation momentum and argue
that one can consider only within the shock wave approximation.Comment: 40pp.,9 figures in eps file
Design and implementation of a twin-family database for behavior genetics and genomics studies.
In this article we describe the design and implementation of a database for extended twin families. The database does not focus on probands or on index twins, as this approach becomes problematic when larger multigenerational families are included, when more than one set of multiples is present within a family, or when families turn out to be part of a larger pedigree. Instead, we present an alternative approach that uses a highly flexible notion of persons and relations. The relations among the subjects in the database have a one-to-many structure, are user-definable and extendible and support arbitrarily complicated pedigrees. Some additional characteristics of the database are highlighted, such as the storage of historical data, predefined expressions for advanced queries, output facilities for individuals and relations among individuals and an easy-to-use multi-step wizard for contacting participants. This solution presents a flexible approach to accommodate pedigrees of arbitrary size, multiple biological and nonbiological relationships among participants and dynamic changes in these relations that occur over time, which can be implemented for any type of multigenerational family study
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