Motivic multiple zeta values and superstring amplitudes

By O. Schlotterer, S. Stieberger. 2012

209 citations recorded by the source corpus.

The structure of tree-level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows one to disentangle its α′-expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the α′-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the α′-expansion onto a non-commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the α′-expansion assumes a very simple and symmetric form, which carries all the relevant information. Equipped with these results we can also cast the closed superstring amplitude into a very elegant form.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/d09f366690aa046bc75d893e4d8a2a0a69ee4c59

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Citations in the corpus

Hexagon functions and the three-loop remainder function (2013, unknown): “The coproduct on multiple polylogarithms has been used in a variety of contexts [35, 82–86].”
Closed string amplitudes as single-valued open string amplitudes (2014, background): “1) enters [11,10], closed superstring tree–level amplitudes exhibit only a subset of MZVs appearing in their α–expansion [11,10].”
Double copy for massive quantum particles with spin (2019, result): “Not only does it follow from the work of KLT [14], but also more recent results show that the double-copy structure permeates all types of strings: the bosonic, heterotic, closed and open superstrings [109–115].”
PolyLogTools — polylogs for the masses (2019, methodology): “tions of symbols in the literature. An important feature of the implementation of the symbol map in PolyLogTools is that it does not put to zero symbol tensors that contain a constant letter, e.g., In[14]:= SymbolMap[ Log[2]*Log[x] ] Out[14]:= CiTi[2,x] + CiTi[x,2] Keeping constant letters in the sy”
Polylogarithms, multiple zeta values and superstring amplitudes (2013, methodology): “The systematics of the appearance of MZVs in disk amplitudes has been analyzed in [12].”