MODULAR INVARIANCE, FINITENESS, AND MISALIGNED SUPERSYMMETRY - NEW CONSTRAINTS ON THE NUMBERS OF PHYSICAL STRING STATES

We investigate the generic distribution of bosonic and fermionic state s at all mass levels in non-supersymmetric string theories, and find t hat a hidden ''misaligned supersymmetry'' must always appear in the st ring spectrum. We show that this misaligned supersymmetry is ultimatel y responsible for the finiteness of string amplitudes in the absence o f full spacetime supersymmetry, and therefore the existence of misalig ned supersymmetry provides a natural constraint on the degree to which spacetime supersymmetry can be broken in string theory without destro ying the finiteness of string amplitudes. Misaligned supersymmetry als o explains how the requirements of modular invariance and absence of p hysical tachyons generically affect the distribution of states through out the string spectrum, and implicitly furnishes a two-variable gener alization of some well-known results in the theory of modular function s.