2,932 research outputs found
On Perturbative Gravity and Gauge Theory
We review some applications of tree-level (classical) relations between
gravity and gauge theory that follow from string theory. Together with
-dimensional unitarity, these relations can be used to perturbatively
quantize gravity theories, i.e. they contain the necessary information for
obtaining loop contributions. We also review recent applications of these ideas
showing that N=1 D=11 supergravity diverges, and review arguments that N=8 D=4
supergravity is less divergent than previously thought, though it does appear
to diverge at five loops. Finally, we describe field variables for the
Einstein-Hilbert Lagrangian that help clarify the perturbative relationship
between gravity and gauge theory.Comment: Talk presented at Third Meeting on Constrained Dynamics and Quantum
Gravity, Villasimius (Sardinia, Italy) September 13-17, 1999 and at the
Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, University of
Adelaide (Australia) December 13-22, 1999. Latex, 9 page
Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and
Witten, I give a compact, manifestly Lorentz-invariant form for tree-level
gauge-theory amplitudes with three opposite helicities.Comment: 12 pages, 1 figur
Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
By exploiting relations between gravity and gauge theories, we present two
infinite sequences of one-loop n-graviton scattering amplitudes: the `maximally
helicity-violating' amplitudes in N=8 supergravity, and the `all-plus' helicity
amplitudes in gravity with any minimally coupled massless matter content. The
all-plus amplitudes correspond to self-dual field configurations and vanish in
supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT)
relations between open and closed string theory amplitudes, which in the
low-energy limit imply relations between gravity and gauge theory tree
amplitudes. For n < 7, we determine the all-plus amplitudes explicitly from
their unitarity cuts. The KLT relations, applied to the cuts, allow us to
extend to gravity a previously found `dimension-shifting' relation between (the
cuts of) the all-plus amplitudes in gauge theory and the maximally
helicity-violating amplitudes in N=4 super-Yang-Mills theory. The gravitational
version of the relation lets us determine the n < 7 N=8 supergravity amplitudes
from the all-plus gravity amplitudes. We infer the two series of amplitudes for
all n from their soft and collinear properties, which can also be derived from
gauge theory using the KLT relations.Comment: Minor errors corrected, Latex, 53 page
One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity
We present an ansatz for all one-loop amplitudes in pure Einstein gravity for
which the n external gravitons have the same outgoing helicity. These loop
amplitudes, which are rational functions of the momenta, also arise in the
quantization of self-dual gravity in four-dimensional Minkowski space. Our
ansatz agrees with explicit computations via D-dimensional unitarity cuts for n
less than or equal to 6. It also has the expected analytic behavior, for all n,
as a graviton becomes soft, and as two momenta become collinear. The gravity
results are closely related to analogous amplitudes in (self-dual) Yang-Mills
theory.Comment: Latex2e, 13 pages with 2 encapsulated figures. Minor corrections mad
Perturbative Relations between Gravity and Gauge Theory
We review the relations that have been found between multi-loop scattering
amplitudes in gauge theory and gravity, and their implications for ultraviolet
divergences in supergravity.Comment: LaTex with package axodraw.sty. 10 pages. Presented by L.D. at
Strings 99. Cosmetic changes onl
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
Regression Depth and Center Points
We show that, for any set of n points in d dimensions, there exists a
hyperplane with regression depth at least ceiling(n/(d+1)). as had been
conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n
hyperplanes in d dimensions there exists a point that cannot escape to infinity
without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our
approach to related questions on the existence of partitions of the data into
subsets such that a common plane has nonzero regression depth in each subset,
and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure
Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
Infrared equations and dual conformal constraints arise as consistency
conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions
are linear relations between leading singularities, which can be computed in
the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently.
Examples for infrared equations have been shown to be implied by global residue
theorems in the Grassmannian picture. Both dual conformal constraints and
infrared equations are mapped explicitly to global residue theorems for
one-loop next-to-maximally-helicity-violating amplitudes. In addition, the
identity relating the BCFW and its parity-conjugated form of tree-level
amplitudes, is shown to emerge from a particular combination of global residue
theorems.Comment: 21 page
Multiple Singular Emission in Gauge Theories
I derive a class of functions unifying all singular limits for the emission
of a given number of soft or collinear gluons in tree-level gauge-theory
amplitudes. Each function is a generalization of the single-emission antenna
function of ref. [1]. The helicity-summed squares of these functions are thus
also generalizations to multiple singular emission of the Catani--Seymour
dipole factorization function.Comment: Corrections for final journal version (sign in eqn. (6.11), equation
references, typos in indices) & removal of comment about FD
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