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One-loop Double Copy Relation from Twisted (Co)homology
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We propose a geometric relation between closed and open string amplitudes at one-loop. After imposing a homological splitting on the world-sheet torus twisted intersection theory is used to establish a one-loop double copy relation. The latter expresses a closed string amplitude by a pair of open string amplitudes and twisted intersection numbers. These inner products on the vector space of allowed differential forms are related to the twisted homology and cohomology groups associated with the Riemann-Wirtinger integral.
Forward citations
Cited by 2 Pith papers
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A double copy from twisted (co)homology at genus g
A double-copy (KLT-type) formula for genus-g hypergeometric integrals is derived from twisted homology intersection numbers and verified numerically at genus two.
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Associators for AdS string amplitude building blocks
Open-string AdS building blocks can be generated by Drinfeld associator recursions and closed-string ones by Deligne associator recursions, yielding all-order zeta-valued expansions.
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