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Closed strings as single-valued open strings: a genus-zero derivation

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Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that tree-level amplitudes of closed and open strings… Click to show full abstract

Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that tree-level amplitudes of closed and open strings are related through the single-valued map `sv'. This relation can be traced back to the underlying moduli-space integrals over punctured Riemann surfaces of genus zero. The sphere integrals $J$ in closed-string amplitudes and the disk integrals $Z$ in open-string amplitudes are shown to obey $J = {\rm sv} \, Z$.

Keywords: genus zero; open strings; single valued; derivation; closed strings

Journal Title: Journal of Physics A: Mathematical and Theoretical
Year Published: 2019

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