1,063 research outputs found
On the Coupling of Gravitons to Matter
Using relationships between open and closed strings, we present a
construction of tree-level scattering amplitudes for gravitons minimally
coupled to matter in terms of gauge theory partial amplitudes. In particular,
we present examples of amplitudes with gravitons coupled to vectors or to a
single fermion pair. We also present two examples with massive graviton
exchange, as would arise in the presence of large compact dimensions. The gauge
charges are represented by flavors of dynamical scalars or fermions. This also
leads to an unconventional decomposition of color and kinematics in gauge
theories.Comment: RevTex, 4 page
A technique for loop calculations in non-Abelian gauge theories - with application to five gluon amplitude
A powerful tool for calculations in non-Abelian gauge theories is obtained by
combining the background field gauge, the helicity basis and the color
decomposition methods. It has reproduced the one-loop calculation of the
five-gluon amplitudes in QCD, is applicable to electroweak processes and
extendable to two-loop calculations.Comment: Latex 22 pages, 3 figure
Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition
We provide efficient constant factor approximation algorithms for the
problems of finding a hierarchical clustering of a point set in any metric
space, minimizing the sum of minimimum spanning tree lengths within each
cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of
cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can
also be used to provide a pants decomposition, that is, a set of disjoint
simple closed curves partitioning the plane minus the input points into subsets
with exactly three boundary components, with approximately minimum total
length. In the Euclidean case, these curves are squares; in the hyperbolic
case, they combine our Euclidean square pants decomposition with our tree
clustering method for general metric spaces.Comment: 22 pages, 14 figures. This version replaces the proof of what is now
Lemma 5.2, as the previous proof was erroneou
Supersymmetry Relations Between Contributions To One-Loop Gauge Boson Amplitudes
We apply ideas motivated by string theory to improve the calculational
efficiency of one-loop weak interaction processes with massive external gauge
bosons. In certain cases ``supersymmetry'' relations between diagrams with a
fermion loop and with a gauge boson loop hold. This is explicitly illustrated
for a particular one-loop standard model process with four-external gauge
bosons. The supersymmetry relations can be used to provide further significant
improvements in calculational efficiency.Comment: 21 pages of plain TeX + 5 PostScript figures (compressed and
uuencoded), UCLA/93/TEP/36 and DTP/93/8
Simplifying Algebra in Feynman Graphs, Part III: Massive Vectors
A T-dualized selfdual inspired formulation of massive vector fields coupled
to arbitrary matter is generated; subsequently its perturbative series modeling
a spontaneously broken gauge theory is analyzed. The new Feynman rules and
external line factors are chirally minimized in the sense that only one type of
spin index occurs in the rules. Several processes are examined in detail and
the cross-sections formulated in this approach. A double line formulation of
the Lorentz algebra for Feynman diagrams is produced in this formalism, similar
to color ordering, which follows from a spin ordering of the Feynman rules. The
new double line formalism leads to further minimization of gauge invariant
scattering in perturbation theory. The dualized electroweak model is also
generated.Comment: 39 pages, LaTeX, 8 figure
Multiloop Calculations in the String-Inspired Formalism: The Single Spinor-Loop in QED
We use the worldline path-integral approach to the Bern-Kosower formalism for
developing a new algorithm for calculation of the sum of all diagrams with one
spinor loop and fixed numbers of external and internal photons. The method is
based on worldline supersymmetry, and on the construction of generalized
worldline Green functions. The two-loop QED -- function is calculated
as an example.Comment: uuencoded ps-file, 20 pages, 2 figures, final revised version to
appear in Phys. Rev.
Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
We present a definition of the four-dimensional helicity (FDH) regularization
scheme valid for two or more loops. This scheme was previously defined and
utilized at one loop. It amounts to a variation on the standard 't
Hooft-Veltman scheme and is designed to be compatible with the use of helicity
states for "observed" particles. It is similar to dimensional reduction in that
it maintains an equal number of bosonic and fermionic states, as required for
preserving supersymmetry. Supersymmetry Ward identities relate different
helicity amplitudes in supersymmetric theories. As a check that the FDH scheme
preserves supersymmetry, at least through two loops, we explicitly verify a
number of these identities for gluon-gluon scattering (gg to gg) in
supersymmetric QCD. These results also cross-check recent non-trivial two-loop
calculations in ordinary QCD. Finally, we compute the two-loop shift between
the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is
identical to the one for dimensional reduction. The two-loop coupling shifts
are then used to obtain the three-loop QCD beta function in the FDH and
dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include
One-loop corrections to the D3 brane action
We calculate one-loop corrections to the effective Lagrangian for the D3
brane. We perform the gauge-fixing of the kappa-symmetric Born-Infeld D3 brane
action in the flat background using Killing gauge. The linearized supersymmetry
of the gauge-fixed action coincides with that of the N=4 Yang-Mills theory. We
use the helicity amplitude and unitarity technique to calculate the one-loop
amplitudes at order alpha^4. The counterterms and the finite 1-loop corrections
are of the form (dF)^4 and their supersymmetric generalization. This is to be
contrasted with the Born-Infeld action which contains (F)^4 and other terms
which do not depend on derivatives of the vector field strength.Comment: 21 pages, LaTex with Axodraw figures. In the revised version new
references have been adde
Simplifying Algebra in Feynman Graphs, Part I:Spinors
We present a general formalism for simplifying manipulations of spin indices
of massless and massive spinors and vectors in Feynman diagrams. The formalism
is based on covariantly reducing the number of field components in the action
in favor of chiral/self-dual fields. In this paper we concentrate on
calculational simplifications involving fermions in gauge theories by
eliminating half of the components of Dirac spinors. Some results are: (1) We
find reference momenta for massless fermions analogous to those used for
external gauge bosons. (2) Many of the known supersymmetry identities (tree and
one-loop) are seen in a simple manner from the graphs. (3) Manipulations with
external line factrs for massive fermions are unnecessary. (4) Some of the
simplifications for nearly maximally helicity violating gluonic amplitudes are
built into the Feynman rules.Comment: 14 pg., plain tex, references adde
The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
Infrared divergences in scattering amplitudes arise when a loop momentum
becomes collinear with a massless external momentum . In gauge
theories, it is known that the L-loop logarithm of a planar amplitude has much
softer infrared singularities than the L-loop amplitude itself. We argue that
planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected
behavior as already at the level of the integrand. Moreover,
we conjecture that the four-point integrand can be uniquely determined, to any
loop-order, by imposing the correct soft-behavior of the logarithm together
with dual conformal invariance and dihedral symmetry. We use these simple
criteria to determine explicit formulae for the four-point integrand through
seven-loops, finding perfect agreement with previously known results through
five-loops. As an input to this calculation we enumerate all four-point dual
conformally invariant (DCI) integrands through seven-loops, an analysis which
is aided by several graph-theoretic theorems we prove about general DCI
integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive
non-zero contributions from 229 and 1873 individual DCI diagrams respectively.Comment: 27 pages, 48 figures, detailed results including PDF and Mathematica
files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7
corrected, Lemma 2 remove
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