We compute the tree-level H2R3 couplings of type II strings and provide some basic tests of the couplings by considering both K3 and Calabi-Yau threefold compactifications. Curiously, additional kinematical structures show up at tree level that are not present in the one-loop couplings. This has interesting implications for type II supersymmetry as well as SL(2,Z) duality in type IIB strings.
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Liu et al. (2021) studied this question.
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