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