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

## TL;DR

This paper introduces twisted elliptic multiple zeta values, generalizing existing concepts, and explores their properties and role in non-planar one-loop open-string amplitudes, revealing new mathematical structures in string theory.

## Contribution

It defines twisted elliptic multiple zeta values, studies their properties, and connects them to non-planar one-loop open-string amplitudes, extending the understanding of elliptic zeta values in string theory.

## Key findings

- Twisted elliptic multiple zeta values degenerate to cyclotomic multiple zeta values at the cusp.
- Properties of twisted elliptic multiple zeta values are characterized.
- Application to non-planar four-point one-loop open-string amplitude is demonstrated.

## 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.