LOOP EXPANSIONS AND STRING 5-BRANE DUALITY

The heterotic string involves two kinds of loop expansion: quantum D = 10 string loops (L) and classical d = 2 sigma-model loops (1). Similarly, the heterotic five-brane requires quantum D = 10 five-brane loops (L') and classical d = 6 sigma-model loops (l'). We show that under string/five-brane duality the roles are reversed: L = l' - 1 and L' = l - 1. Thus the theory may be regarded as purely classical. Assuming L' greater-than-or-equal-to 0, this rules out a cosmological term which can occur only for l = 0.