One-loop masses of Neumann-Dirichlet open strings and boundary-changing vertex operators

TL;DR

This paper calculates one-loop masses of scalars in the Neumann-Dirichlet sector of open strings with broken supersymmetry, using boundary-changing vertex operators, and analyzes their stability and potential for tachyon-free configurations.

Contribution

It introduces a method to compute one-loop masses via boundary-changing vertex operators in a specific orientifold setup with broken supersymmetry.

Findings

Masses reduce to simple forms at the supersymmetry breaking scale

Identifies brane configurations without tachyons at one loop

Provides conditions for stable, runaway, or positive potential backgrounds

Abstract

We derive the masses acquired at one loop by massless scalars in the Neumann-Dirichlet sector of open strings, when supersymmetry is spontaneously broken. It is done by computing two-point functions of "boundary-changing vertex operators" inserted on the boundaries of the annulus and M\"obius strip. This requires the evaluation of correlators of "excited boundary-changing fields," which are analogous to excited twist fields for closed strings. We work in the type IIB orientifold theory compactified on $T^2\times T^4/\mathbb{Z}_2$, where $\mathcal{N}=2$ supersymmetry is broken to $\mathcal{N}=0$ by the Scherk-Schwarz mechanism implemented along $T^2$. Even though the full expression of the squared masses is complicated, it reduces to a very simple form when the lowest scale of the background is the supersymmetry breaking scale $M_{3/2}$. We apply our results to analyze in this regime the stability at the quantum level of the moduli fields arising in the Neumann-Dirichlet sector. This completes the study of Ref. [32], where the quantum masses of all other types of moduli arising in the open- or closed-string sectors are derived. Ultimately, we identify all brane configurations that produce backgrounds without tachyons at one loop and yield an effective potential exponentially suppressed, or strictly positive with runaway behavior of $M_{3/2}$.