Misaligned Supersymmetry and Open Strings

TL;DR

This paper explores how misaligned supersymmetry causes cancellations between bosons and fermions in non-supersymmetric string theories, including open strings, leading to a suppressed growth rate of states and potential insights into the absence of observed supersymmetry.

Contribution

It demonstrates that misaligned supersymmetry induces cancellations in open-string theories and proves the complete cancellation for a broad class of models, advancing understanding of non-supersymmetric string landscapes.

Findings

Misaligned supersymmetry causes cancellations between bosons and fermions at different energy levels.

The growth rate of states is dominated by e^{C_eff√n} with C_eff< C_tot.

Complete cancellation (C_eff=0) is proven for a wide class of models.

Abstract

The study of non-supersymmetric string theories is shedding light on an important corner of the string landscape and might ultimately explain why, so far, we did not observe supersymmetry in our universe. We review how misaligned supersymmetry in closed-string theories leads to a cancellation between bosons and fermions even in non-supersymmetric string theories. We then show that the same cancellation takes place for open strings by studying an anti-D$p$-brane placed on top of an O$p$-plane in type II string theory. Misaligned supersymmetry consists in cancellations between bosons and fermions at \emph{different} energy levels, in such a way that the averaged number of states grows at a rate dominated by a factor $\mathrm{e}^{C_{\mathrm{eff}}\sqrt{n}}$, with $C_{\mathrm{eff}}<C_{\mathrm{tot}}$, where $C_{\mathrm{tot}}$ is the inverse Hagedorn temperature. We prove the previously conjectured complete cancellation, i.e. we prove that $C_{\mathrm{eff}}=0$, for a vast class of models.