Modular invariance, misalignment and finiteness in non-supersymmetric strings

TL;DR

This paper demonstrates how modular invariance and misaligned supersymmetry collaborate to ensure finiteness in non-supersymmetric string theories, especially in controlling divergences in the one-loop cosmological constant.

Contribution

It reveals the role of modular invariance in open-string models and connects misaligned supersymmetry with the cancellation of divergences in non-supersymmetric strings.

Findings

Exponential divergences in the cosmological constant are canceled by modular invariance.

Misaligned supersymmetry predicts non-exponential growth of states, aiding finiteness.

Modular structure explains the absence of power-law divergences.

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.