39 research outputs found
Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
A formalism is provided to calculate tree amplitudes in open superstring
theory for any multiplicity at any order in the inverse string tension. We
point out that the underlying world-sheet disk integrals share substantial
properties with color-ordered tree amplitudes in Yang-Mills field theories. In
particular, we closely relate world-sheet integrands of open-string tree
amplitudes to the Kawai-Lewellen-Tye representation of supergravity amplitudes.
This correspondence helps to reduce the singular parts of world-sheet disk
integrals -including their string corrections- to lower-point results. The
remaining regular parts are systematically addressed by polylogarithm
manipulations.Comment: 79 pages, LaTeX; v2: final version to appear in Fortschritte der
Physik; for additional material, see: http://mzv.mpp.mpg.d
Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
We introduce a class of iterated integrals that generalize multiple
polylogarithms to elliptic curves. These elliptic multiple polylogarithms are
closely related to similar functions defined in pure math- ematics and string
theory. We then focus on the equal-mass and non-equal-mass sunrise integrals,
and we develop a formalism that enables us to compute these Feynman integrals
in terms of our iterated integrals on elliptic curves. The key idea is to use
integration-by-parts identities to identify a set of integral kernels, whose
precise form is determined by the branch points of the integral in question.
These kernels allow us to express all iterated integrals on an elliptic curve
in terms of them. The flexibility of our approach leads us to expect that it
will be applicable to a large variety of integrals in high-energy physics.Comment: 22 page
A dictionary between R-operators, on-shell graphs and Yangian algebras
We translate between different formulations of Yangian invariants relevant
for the computation of tree-level scattering amplitudes in N=4
super-Yang--Mills theory. While the R-operator formulation allows to relate
scattering amplitudes to structures well known from integrability, it can
equally well be connected to the permutations encoded by on-shell graphs.Comment: 44 pages; replaced with published versio
All order alpha'-expansion of superstring trees from the Drinfeld associator
We derive a recursive formula for the alpha'-expansion of superstring tree
amplitudes involving any number N of massless open string states. String
corrections to Yang-Mills field theory are shown to enter through the Drinfeld
associator, a generating series for multiple zeta values. Our results apply for
any number of spacetime dimensions or supersymmetries and chosen helicity
configurations.Comment: 6 pages, LaTeX; v2: Final version to appear in PR
A KLT-like construction for multi-Regge amplitudes
Inspired by the calculational steps originally performed by Kawai, Lewellen
and Tye, we decompose scattering amplitudes with single-valued coefficients
obtained in the multi-Regge-limit of N=4 super-Yang-Mills theory into products
of scattering amplitudes with multi-valued coefficients. We consider the
simplest non-trivial situation: the six-point remainder function complementing
the Bern-Dixon-Smirnov ansatz for multi-loop amplitudes. Utilizing inverse
Mellin transformations, all single-valued amplitude components can indeed be
decomposed into multi-valued amplitude components. Although the final
expression is very similar in structure to the Kawai-Lewellen-Tye construction,
moving away from the highly symmetric string scenario comes with several
imponderabilities, some of which become more pronounced when considering more
than six external legs in the remainder function.Comment: 39 pages, 11 figures, 3 appendice