11-DIMENSIONAL ORIGIN OF STRING STRING DUALITY - A ONE-LOOP TEST/

Membrane/fivebrane duality in D = 11 implies Type IIA string/Type IIA fivebrane duality in D = 10, which in turn implies Type IIA string/het erotic string duality in D = 6. To test the conjecture, we reproduce t he corrections to the S-form field equations of the D = 10 Type IIA st ring (a mixture of tree-level and one-loop effects) starting from the Chern-Simons corrections to the 7-form Bianchi identities of the D = 1 1 fivebrane (a purely tree-level effect). K3 compactification of the l atter then yields the familiar gauge and Lorentz Chem-Simons correctio ns to 3-form Bianchi identities of the heterotic string. We note that the absence of a dilaton in the D = 11 theory allows us to fix both th e gravitational constant and the fivebrane tension in terms of the mem brane tension. We also comment on an apparent conflict between fundame ntal and solitonic heterotic strings and on the puzzle of a fivebrane origin of S-duality.