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

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Schlotterer,  Oliver
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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1808.00713.pdf
(Preprint), 316KB

JPA_52_045401.pdf
(Publisher version), 2MB

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Citation

Schlotterer, O., & Schnetz, O. (2019). Closed strings as single-valued open strings: A genus-zero derivation. Journal of physics A, 52(4): 045401. doi:10.1088/1751-8121/aaea14.


Cite as: http://hdl.handle.net/21.11116/0000-0001-FA37-8
Abstract
Based on general mathematical assumptions we give an independent, elementary proof 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 $J = {\rm sv} \, Z$.