Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes

Abstract

We consider a generalization of elliptic multiple zeta values, which we call twisted elliptic multiple zeta values. These arise as iterated integrals on an elliptic curve from which a rational lattice has been removed. At the cusp, twisted elliptic multiple zeta values are shown to degenerate to cyclotomic multiple zeta values in the same way as elliptic multiple zeta values degenerate to classical multiple zeta values. We investigate properties of twisted elliptic multiple zeta values and consider them in the context of the non-planar part of the four-point one-loop open-string amplitude.

28 + 19 pages, 6 figures, v2: explanations added, published version

References in corpus (5)

• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Multi-Gluon Scattering in Open Superstring Theory
• Supersymmetry Relations and MHV Amplitudes in Superstring Theory
• On the algebraic structure of iterated integrals of quasimodular forms
• Multiple polylogarithm values at roots of unity

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