80 research outputs found
The No-Triangle Hypothesis for N=8 Supergravity
We study the perturbative expansion of N=8 supergravity in four dimensions
from the viewpoint of the ``no-triangle'' hypothesis, which states that
one-loop graviton amplitudes in N=8 supergravity only contain scalar box
integral functions. Our computations constitute a direct proof at six-points
and support the no-triangle conjecture for seven-point amplitudes and beyond.Comment: 43page
Efficient analytic computation of higher-order QCD amplitudes
URL: http://www-spht.cea.fr/articles/t95/026/ Le calcul analytique efficace des amplitudes aux ordres supérieurs en QCDWe review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints
Infrared behavior of graviton-graviton scattering
The quantum effective theory of general relativity, independent of the
eventual full theory at high energy, expresses graviton-graviton scattering at
one loop order O(E^4) with only one parameter, Newton's constant. Dunbar and
Norridge have calculated the one loop amplitude using string based techniques.
We complete the calculation by showing that the 1/(d-4) divergence which
remains in their result comes from the infrared sector and that the cross
section is finite and model independent when the usual bremsstrahlung diagrams
are included.Comment: 12 pages, uses axodra
MHV-Vertices for Gravity Amplitudes
We obtain a CSW-style formalism for calculating graviton scattering
amplitudes and prove its validity through the use of a special type of
BCFW-like parameter shift. The procedure is illustrated with explicit examples.Comment: 21 pages, minor typos corrected, proof added in section
Inherited Twistor-Space Structure of Gravity Loop Amplitudes
At tree-level, gravity amplitudes are obtainable directly from gauge theory
amplitudes via the Kawai, Lewellen and Tye closed-open string relations. We
explain how the unitarity method allows us to use these relations to obtain
coefficients of box integrals appearing in one-loop N=8 supergravity amplitudes
from the recent computation of the coefficients for N=4 super-Yang-Mills
non-maximally-helicity-violating amplitudes. We argue from factorisation that
these box coefficients determine the one-loop N=8 supergravity amplitudes,
although this remains to be proven. We also show that twistor-space properties
of the N=8 supergravity amplitudes are inherited from the corresponding
properties of N=4 super-Yang-Mills theory. We give a number of examples
illustrating these ideas.Comment: 32 pages, minor typos correcte
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
Poincare Polynomials and Level Rank Dualities in the Coset Construction
We review the coset construction of conformal field theories; the emphasis is
on the construction of the Hilbert spaces for these models, especially if fixed
points occur. This is applied to the superconformal cosets constructed by
Kazama and Suzuki. To calculate heterotic string spectra we reformulate the
Gepner con- struction in terms of simple currents and introduce the so-called
extended Poincar\'e polynomial. We finally comment on the various equivalences
arising between models of this class, which can be expressed as level rank
dualities. (Invited talk given at the III. International Conference on
Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June
1993. To appear in Theor. Math. Phys.)Comment: 14 pages in LaTeX, HD-THEP-93-4
One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory
We use Supersymmetric Ward Identities and quadruple cuts to generate n-pt
NMHV amplitudes involving gluinos and adjoint scalars from purely gluonic
amplitudes. We present a set of factors that can be used to generate one-loop
NMHV amplitudes involving gluinos or adjoint scalars in N=4 Super Yang-Mills
from the corresponding purely gluonic amplitude.Comment: 16 pages, JHEP versio
On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
String theory implies that field theories containing gravity are in a certain
sense `products' of gauge theories. We make this product structure explicit up
to two loops for the relatively simple case of N=8 supergravity four-point
amplitudes, demonstrating that they are `squares' of N=4 super-Yang-Mills
amplitudes. This is accomplished by obtaining an explicit expression for the
-dimensional two-loop contribution to the four-particle S-matrix for N=8
supergravity, which we compare to the corresponding N=4 Yang-Mills result. From
these expressions we also obtain the two-loop ultraviolet divergences in
dimensions D=7 through D=11. The analysis relies on the unitarity cuts of the
two theories, many of which can be recycled from a one-loop computation. The
two-particle cuts, which may be iterated to all loop orders, suggest that
squaring relations between the two theories exist at any loop order. The
loop-momentum power-counting implied by our two-particle cut analysis indicates
that in four dimensions the first four-point divergence in N=8 supergravity
should appear at five loops, contrary to the earlier expectation, based on
superspace arguments, of a three-loop counterterm.Comment: Latex, 52 pages, discussion of 2 loop divergences in D=8,10 adde
Recursive Calculation of One-Loop QCD Integral Coefficients
We present a new procedure using on-shell recursion to determine coefficients
of integral functions appearing in one-loop scattering amplitudes of gauge
theories, including QCD. With this procedure, coefficients of integrals,
including bubbles and triangles, can be determined without resorting to
integration. We give criteria for avoiding spurious singularities and boundary
terms that would invalidate the recursion. As an example where the criteria are
satisfied, we obtain all cut-constructible contributions to the one-loop
n-gluon scattering amplitude, A_n^{oneloop}(...--+++...), with split-helicity
from an N=1 chiral multiplet and from a complex scalar. Using the
supersymmetric decomposition, these are ingredients in the construction of QCD
amplitudes with the same helicities. This method requires prior knowledge of
amplitudes with sufficiently large numbers of legs as input. In many cases,
these are already known in compact forms from the unitarity method.Comment: 36 pages; v2 clarification added and typos fixed, v3 typos fixe
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