Tachyons and Misaligned Supersymmetry in Closed String Vacua

TL;DR

This paper explores the relationship between tachyons, supersymmetry misalignment, and stability in closed string vacua, demonstrating that the growth rate of boson-fermion oscillations is determined by the lightest state and confirming Dienes' conjecture on stability conditions.

Contribution

It proves that boson-fermion oscillations occur even with tachyons and links the growth rate to the lightest state, confirming the conjecture that stability requires vanishing sector averages.

Findings

Oscillations occur even with tachyons present.

Growth rate C_{eff} is set by the lightest state.

Classical stability requires vanishing sector averages.

Abstract

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 C_{eff} smaller than the expected inverse Hagedorn temperature. Dienes also conjectured that C_{eff} should vanish when tachyons are absent. In this paper, we revisit this problem and show that boson-fermion oscillations are realised even when tachyons are present in the physical spectrum. In fact, we prove that the average growth rate C_{eff} is set by the mass of the lightest state, be it massless or tachyonic, and coincides with the effective inverse Hagedorn temperature of the associated thermal theory. We also provide a general proof that the necessary and sufficient condition for classical stability is the vanishing of the sector averaged sum which implies C_{eff}=0, in agreement with Dienes' conjecture.