On the quantum stability of IIB orbifolds and orientifolds with Scherk-Schwarz SUSY breaking

TL;DR

This paper investigates the quantum stability of Type IIB orbifold and orientifold models with Scherk-Schwarz supersymmetry breaking, analyzing how the vacuum energy density varies with the circle radius and identifying conditions for stability or instability.

Contribution

It provides a detailed analysis of the R-dependence of the one-loop vacuum energy in various Type IIB models with Scherk-Schwarz SUSY breaking, highlighting different behaviors for Z2 and non-Z2 twists.

Findings

For non-Z2 twists, the vacuum energy is always negative and leads to tachyonic instability.

Z2 orientifold models can have stable minima or runaway behavior depending on parameters.

A 4D chiral orientifold model shows a tendency towards instability or decompactification as moduli vary.

Abstract

We study the quantum stability of Type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken {\it \`a la} Scherk-Schwarz (SS) by twisting periodicity conditions along a circle of radius R. In particular, we compute the R-dependence of the one-loop induced vacuum energy density $\rho(R)$, or cosmological constant. For SS twists different from Z2 we always find, for both orbifolds and orientifolds, a monotonic $\rho(R)<0$, eventually driving the system to a tachyonic instability. For Z2 twists, orientifold models can have a different behavior, leading either to a runaway decompactification limit or to a negative minimum at a finite value R_0. The last possibility is obtained for a 4D chiral orientifold model where a more accurate but yet preliminary analysis seems to indicate that $R_0\to \infty$ or towards the tachyonic instability, as the dependence on the other geometric moduli is included.