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Single-valued integration and superstring amplitudes in genus zero. (English) Zbl 1483.81117

String amplitudes describe the interactions between states in string theory and are one of the most important observables. Indeed, they allow to reconstruct the low-energy effective action of string theory and to understand how the latter departs from usual local QFT. Moreover, these amplitudes display deep mathematical properties as they are obtained by integrating appropriate form over moduli spaces of Riemann surfaces. This paper studies open and closed string amplitudes with an arbitrary number of external states using the method of single-valued integration developed by the authors in a previous paper. The objective is to prove rigorously several properties of the amplitudes:
1.
Defining a “canonical regularisation [string amplitudes] at tree level.”
2.
Proving that the amplitudes “admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values.”
3.
Showing that “closed string amplitudes are the single-valued projections of (motivic lifts of) open string amplitudes.”
4.
Proving of the “KLT formula expressing closed string amplitudes as quadratic expressions in open string amplitudes.”

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
11M32 Multiple Dirichlet series and zeta functions and multizeta values
14H81 Relationships between algebraic curves and physics
33B15 Gamma, beta and polygamma functions

Software:

HyperInt; MPL
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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