Tachyons and misaligned supersymmetry in closed string vacua

In a remarkable paper, Dienes discovered that the absence of physical tachyons in closed string theory is intimately related to oscillations in the net number of bosonic minus fermionic degrees of freedom, a pattern predicted by an underlying misaligned supersymmetry. The average of these oscillations was linked to an exponential growth controlled by an effective central charge Ceff smaller than the expected inverse Hagedorn temperature. Dienes also conjectured that Ceff should vanish when tachyons are absent.