Abstract
In this article we show that finite perturbative corrections in non-supersymmetric strings can be understood via an interplay between modular invariance and misaligned supersymmetry. While modular invariance is known to be crucial in closed-string models, its presence and role for open strings is more subtle. Nevertheless, we argue that it leads to cancellations in physical quantities such as the one-loop cosmological constant and prevents them from diverging. In particular, we show that if the sector-averaged number of states does not grow exponentially, as predicted by misaligned supersymmetry, all exponential divergences in the one-loop cosmological constant cancel out as well. To account for the absence of power-law divergences, instead, we need to resort to the modular structure of the partition function. We finally comment on the presence of misaligned supersymmetry in the known 10-dimensional tachyon-free non-supersymmetric string theories.
Highlights
In this article we show that finite perturbative corrections in non-supersymmetric strings can be understood via an interplay between modular invariance and misaligned supersymmetry
The role of modular invariance in ensuring finiteness is well-known for closed string theories, we prove that similar cancellations hold for open strings
Whilst we showed explicitly how misaligned state degeneracies lead to a cancellation of exponential divergences in the open string one-loop cosmological constant, we used modular invariance to prove that the polynomial divergences cancel
Summary
The mathematical structure underlying superstring theory has received a tremendous and well-deserved amount of attention. Dienes defined a sector-average net degeneracy an , and proved that for oriented closed string theories, the exponential growth in an is always slower than the growth in the individual sectors, an ∼ eCeff n with Ceff < C, provided modular invariance and the absence of physical tachyons. While the heterotic SO(16)×SO(16)-theory and the Sugimoto model have their entire spectrum in a standardly or misalignedly supersymmetric phase, and do exhibit misaligned supersymmetry, this is not the case for the type 0 B theory The latter is somewhat special since it presents misaligned supersymmetry only in the open-string sector (annulus and Möbius strip), whereas its closed-string sector does not present any sort of supersymmetry whatsoever, containing only bosons. Appendix A reviews useful properties of special functions appearing in misaligned supersymmetry and appendix B contains additional computational details
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