Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes

Abstract

In this PhD thesis we study holomorphic and non-holomorphic elliptic analogues of multiple zeta values, namely elliptic multiple zeta values and modular graph functions. Both classes of functions have been discovered very recently, and are involved in the computation of genus one superstring amplitudes. In particular, we obtain new results on the asymptotic expansion of these functions that allow us to perform explicit computations and point out analogies between genus zero and genus one amplitudes.

arXiv commentPhD thesis, 126 pages, Bonn, 2018. - Diss., Univ. Bonn, 2017. - urn:nbn:de:hbz:5n-50006

References in corpus (12)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Motivic Multiple Zeta Values and Superstring Amplitudes
• Mixed Tate Motives and Multiple Zeta Values
• Closed String Amplitudes as Single-Valued Open String Amplitudes
• The closed-string 3-loop amplitude and S-duality
• Superstring Perturbation Theory Revisited
• Closed Superstring Amplitudes, Single-Valued Multiple Zeta Values and Deligne Associator
• Supermoduli Space Is Not Projected
• Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus
• The two-loop superstring five-point amplitude and S-duality
• Rational convex cones and cyclotomic multiple zeta values
• Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals

Cited by in corpus (9)

• Eigenvalue equation for the modular graph $C_{a,b,c,d}$
• From Little String Free Energies Towards Modular Graph Functions
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• Genus-zero and genus-one string amplitudes and special multiple zeta values
• Double shuffle relations for arborified zeta values
• Symmetries in A-Type Little String Theories, Part I
• Hyper-Mahler measures via Goncharov-Deligne cyclotomy
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands