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In double field theory, motivated by its field theoretic consistency, thelevel matching condition is generalized to the so-called strong constraint. Inthis note, it is investigated what the two-dimensional conformal field theoryorigin of this constraint is. Initially treating the left- and right-movers asindependent, we compute the torus partition function as well as a generalizedVirasoro-Shapiro amplitude. In non-compact directions the strong constraintarises from the factorization of the Virasoro-Shapiro amplitude over physicalstates as determined by the modular invariant partition function. From the sameargument, along internal toroidal directions, no analogous constraint arises.

A Note on the CFT Origin of the Strong Constraint of DFT