495 research outputs found
Amplitude recursions with an extra marked point
The recursive calculation of Selberg integrals by Aomoto and Terasoma using the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an auxiliary point and facilitates the recursive evaluation of string amplitudes at genus zero: open-string N-point amplitudes can be obtained from those at N-1 points. We establish a similar formalism at genus one, which allows the recursive calculation of genus-one Selberg integrals using an extra marked point in a differential equation of Knizhnik-Zamolodchikov-Bernard type. Hereby genus-one Selberg integrals are related to genus-zero Selberg integrals. Accordingly, N-point open-string amplitudes at genus one can be obtained from (N+2)-point open-string amplitudes at tree level. The construction is related to and in accordance with various recent results in intersection theory and string theory
Relations between elliptic multiple zeta values and a special derivation algebra
We investigate relations between elliptic multiple zeta values and describe a
method to derive the number of indecomposable elements of given weight and
length. Our method is based on representing elliptic multiple zeta values as
iterated integrals over Eisenstein series and exploiting the connection with a
special derivation algebra. Its commutator relations give rise to constraints
on the iterated integrals over Eisenstein series relevant for elliptic multiple
zeta values and thereby allow to count the indecomposable representatives.
Conversely, the above connection suggests apparently new relations in the
derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations
for elliptic multiple zeta values over a wide range of weights and lengths.Comment: 43 pages, v2:replaced with published versio
Engineering orthogonal dual transcription factors for multi-input synthetic promoters
Synthetic biology has seen an explosive growth in the capability of engineering artificial gene circuits from transcription factors (TFs), particularly in bacteria. However, most artificial networks still employ the same core set of TFs (for example LacI, TetR and cI). The TFs mostly function via repression and it is difficult to integrate multiple inputs in promoter logic. Here we present to our knowledge the first set of dual activator-repressor switches for orthogonal logic gates, based on bacteriophage λ cI variants and multi-input promoter architectures. Our toolkit contains 12 TFs, flexibly operating as activators, repressors, dual activator–repressors or dual repressor–repressors, on up to 270 synthetic promoters. To engineer non cross-reacting cI variants, we design a new M13 phagemid-based system for the directed evolution of biomolecules. Because cI is used in so many synthetic biology projects, the new set of variants will easily slot into the existing projects of other groups, greatly expanding current engineering capacities
Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
We investigate Yangian-invariant deformations of one-loop amplitudes in N = 4
super-Yang-Mills theory employing an algebraic representation of amplitudes. In
this language, we reproduce the deformed massless box integral describing the
deformed four-point one-loop amplitude and compare different realizations of
said amplitude.Comment: 19 page
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
Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
We investigate single-valued polylogarithms in two complex variables, which
are relevant for the seven-point remainder function in N=4 super-Yang-Mills
theory in the multi-Regge regime. After constructing these two-dimensional
polylogarithms, we determine the leading logarithmic approximation of the
seven-point remainder function up to and including five loops.Comment: 20 pages, 2 figures; v2: replaced with published versio
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
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