Tachyons and Misaligned Supersymmetry in Closed String Vacua
arXiv:2301.13702 · doi:10.1007/JHEP06(2023)174
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.
arXiv comment32 pages. Improvement based on an exact Rademacher expansion of the Fourier coefficients of characters. Appendix A added. Refs added
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