PUTTING STRING STRING DUALITY TO THE TEST

After simultaneous compactification of spacetime and worldvolume on K3 , the D = 10 heterotic fivebrane with gauge group S0(32) behaves like a D = 6 heterotic string with gauge group S0(28) x SU(2), but with Kac -Moody levels different from those of the fundamental string. Thus the string/fivebrane duality conjecture in D = 10 gets replaced by a stri ng/string duality conjecture in D = 6. Since D = 6 strings are better understood than D = 10 fivebranes, this provides a more reliable labor atory in which to test the conjecture. According to string/string dual ity, the Green-Schwarz factorization of the D = 6 spacetime anomaly po lynomial l(8) into X(4) ($) over tilde X(4) means that just as X(4) is the sigma-model anomaly polynomial of the fundamental string worldshe et so ($) over tilde X4 should be the corresponding polynomial of the dual string worldsheet. To test this idea we perform a classical dual string calculation of ($) over tilde X(4) and find agreement with the quantum fundamental string result. This also provides an a posteriori justification for assumptions made in a previous paper on string/fiveb rane duality. Finally we speculate on the relevance of string/string d uality to the vacuum degeneracy problem.