437 research outputs found
Monodromy and Kawai-Lewellen-Tye Relations for Gravity Amplitudes
We are still learning intriguing new facets of the string theory motivated
Kawai-Lewellen-Tye (KLT) relations linking products of amplitudes in Yang-Mills
theories and amplitudes in gravity. This is very clearly displayed in
computations of N=8 supergravity where the perturbative expansion show a vast
number of similarities to that of N=4 super-Yang-Mills. We will here
investigate how identities based on monodromy relations for Yang-Mills
amplitudes can be very useful for organizing and further streamlining the KLT
relations yielding even more compact results for gravity amplitudes.Comment: 6 pages, 12th Marcel Grossman meeting 200
Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
We analyse one-loop graviton amplitudes in the field theory limit of a
genus-one string theory computation. The considered amplitudes can be
dimensionally reduced to lower dimensions preserving maximal supersymmetry. The
particular case of the one-loop five-graviton amplitude is worked out in detail
and explicitly features no triangle contributions. Based on a recursive form of
the one-loop amplitude we investigate the contributions that will occur at
n-point order in relation to the ``no-triangle'' hypothesis of N=8
supergravity. We argue that the origin of unexpected cancellations observed in
gravity scattering amplitudes is linked to general coordinate invariance of the
gravitational action and the summation over all orderings of external legs.
Such cancellations are instrumental in the extraordinary good ultra-violet
behaviour of N=8 supergravity amplitudes and will play a central role in
improving the high-energy behaviour of gravity amplitudes at more than one
loop.Comment: 25 pages. 2 eps pictures, harvmac format. v2: version to appear in
JHEP. Equations (3.9), (3.12) and minor typos correcte
Absence of Triangles in Maximal Supergravity Amplitudes
From general arguments, we show that one-loop n-point amplitudes in
colourless theories satisfy a new type of reduction formula. These lead to the
existence of cancellations beyond supersymmetry. Using such reduction relations
we prove the no-triangle hypothesis in maximal supergravity by showing that in
four dimensions the n-point graviton amplitude contain only scalar box integral
functions. We also discuss the reduction formulas in the context of gravity
amplitudes with less and no supersymmetry.Comment: 23 pages, RevTeX4 format. v2: Expanded version with a new section
providing some extra background material and an overview of the general
arguments. Minors typos have been corrected. Version to be publishe
On-shell Techniques and Universal Results in Quantum Gravity
We compute the leading post-Newtonian and quantum corrections to the Coulomb
and Newtonian potentials using the full modern arsenal of on-shell techniques;
we employ spinor-helicity variables everywhere, use the Kawai-Lewellen-Tye
(KLT) relations to derive gravity amplitudes from gauge theory and use
unitarity methods to extract the terms needed at one-loop order. We stress that
our results are universal and thus will hold in any quantum theory of gravity
with the same low-energy degrees of freedom as we are considering. Previous
results for the corrections to the same potentials, derived historically using
Feynman graphs, are verified explicitly, but our approach presents a huge
simplification, since starting points for the computations are compact and
tedious index contractions and various complicated integral reductions are
eliminated from the onset, streamlining the derivations. We also analyze the
spin dependence of the results using the KLT factorization, and show how the
spinless correction in the framework are easily seen to be independent of the
interacting matter considered.Comment: 34 pages, 7 figures, typos corrected, published versio
Scattering Equations and String Theory Amplitudes
Scattering equations for tree-level amplitudes are viewed in the context of
string theory. As a result of the comparison we are led to define a new dual
model which coincides with string theory in both the small and large
limit, and whose solution is found algebraically on the surface of solutions to
the scattering equations. Because it has support only on the scattering
equations, it can be solved exactly, yielding a simple resummed model for
-corrections to all orders. We use the same idea to generalize
scattering equations to amplitudes with fermions and any mixture of scalars,
gluons and fermions. In all cases checked we find exact agreement with known
results.Comment: v2: 18 pp, 1 figure, added clarifications and comments. Version to be
published in PR
Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
We discuss monodromy relations between different color-ordered amplitudes in
gauge theories. We show that Jacobi-like relations of Bern, Carrasco and
Johansson can be introduced in a manner that is compatible with these monodromy
relations. The Jacobi-like relations are not the most general set of equations
that satisfy this criterion. Applications to supergravity amplitudes follow
straightforwardly through the KLT-relations. We explicitly show how the
tree-level relations give rise to non-trivial identities at loop level.Comment: 28 pages, 8 figures, JHEP
Minimal Basis for Gauge Theory Amplitudes
Identities based on monodromy for integrations in string theory are used to
derive relations between different color ordered tree-level amplitudes in both
bosonic and supersymmetric string theory. These relations imply that the color
ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal
basis of (n-3)! amplitudes. This result holds for any choice of polarizations
of the external states and in any number of dimensions.Comment: v2: typos corrected, some rephrasing of the general discussion.
Captions to figures added. Version to appear in PRL. 4 pages, 5 figure
Assessing paleotemperature and seasonality during the early Eocene climatic optimum (EECO) in the Belgian basin by means of fish otolith stable O and C isotopes
The Paleogene greenhouse world comprises variable paleoclimate conditions providing an indispensable deep-time perspective for the possible effects of human-induced climate change. In this paper, paleotemperature data of the Early Eocene Climatic Optimum (EECO) from the mid-latitude marginal marine Belgian Basin are discussed. They are derived from fish otolith d18O compositions of four non-migratory species belonging to the families Congridae and Ophidiidae. Otoliths from several levels and localities within the middle to late Ypresian were selected. After manual polishing, bulk and incremental microsamples were drilled and analyzed by a mass spectrometer. A cross-plot of bulk otolith d18O vs. d13C results shows a discrepancy between both families used. Ophidiid data probably represent true bottom water temperatures of the Belgian Basin. The mean annual temperature (MAT) of the EECO is calculated at 27.5 °C, which is in line with other proxy results. However, variations in MAT up to 6 °C occur, suggesting a pronounced expression of climate variability in mid-latitude marginal basins. Incremental analyses revealed a ~9.5 °C mean annual range of temperatures, similar to modern seasonality. These results show that marginal marine environments such as the Belgian Basin are well suited to infer high-resolution paleoclimate variability
Modular graph functions
In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices. Such functions, which we will refer to as modular graph functions, arise, for example, in the low energy expansion of genus-one Type II superstring amplitudes. We here introduce a class of single-valued elliptic multiple polylogarithms, which are defined as elliptic functions associated with Feynman graphs with vanishing external momenta at all but two vertices. These functions depend on a coordinate, ζ, on the elliptic curve and reduce to modular graph functions when ζ is set equal to 1. We demonstrate that these single-valued elliptic multiple polylogarithms are linear combinations of multiple polylogarithms, and that modular graph functions are sums of single-valued elliptic multiple polylogarithms evaluated at the identity of the elliptic curve, in both cases with rational coefficients. This insight suggests the many interrelations between modular graph functions (a few of which were established in earlier papers) may be obtained as a consequence of identities involving multiple polylogarithms, and explains an earlier observation that the coefficients of the Laurent polynomial at the cusp are given by rational numbers times single-valued multiple zeta values
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