Causality and supersymmetry in the superstring theory

Reduction of the ten-dimensional, heterotic-superstring effective action S, including quartic higher-derivative terms R4, yields a physical four-action S which is tachyon-free up to quadratic order R2-the masses M0 and M2 of the spin-0 and spin-2 particles are both real-when the internal six-space is a Calabi-Yau metric g(mu)(nu) and N = 1 supersymmetry is preserved via the equation dH = tr(R ^R) - Tr(F ^F)/30 = 0, where H(mu)(nu)(zeta) is the totally antisymmetric three-index field (while the bosonic string and type-II superstring may contain a spin-2 tachyon and a spin-0 tachyon, respectively). Here, we show that this crucial feature is independent of imposing supersymmetry, for if dH (not equal to) 0, there is an additional contribution to R2 which, however, produces no tachyons. Thus, the requirement of a stable, causal theory singles out the heterotic superstring irrespective of the requirement of N = 1 supersymmetry, which is essential at high energies rather for its roles in the vanishing of the cosmological constant and the maintenance of the gauge hierarchy.