Abstract
We consider an open-string realisation of N=2→N=0 spontaneous breaking of supersymmetry in four-dimensional Minkowski spacetime. It is based on type IIB orientifold theory compactified on T2×T4/Z2, with Scherk–Schwarz supersymmetry breaking implemented along T2. We show that in the regions of moduli space where the supersymmetry breaking scale is lower than the other scales, there exist configurations with minima that have massless Bose-Fermi degeneracy and hence vanishing one-loop effective potential, up to exponentially suppressed corrections. These backgrounds describe non-Abelian gauge theories, with all open-string moduli and blowing up modes of T4/Z2 stabilized, while all untwisted closed-string moduli remain flat directions. Other backgrounds with strictly positive effective potentials exist, where the only instabilities arising at one loop are associated with the supersymmetry breaking scale, which runs away. All of these backgrounds are consistent non-perturbatively.
Highlights
The question of how moduli come to acquire masses in the true vacuum is central in the context of string phenomenology
Non-perturbative effects induce a spontaneous breaking of supersymmetry at a scale much below the string scale Ms [1,2,3,4,5,6], introducing mild instabilities in only a very limited number of moduli that lead to phenomenologically desirable effects such as the BroutEnglert-Higgs mechanism
An alternative and arguably more honest approach is to implement spontaneous supersymmetry breaking from the outset, at the classical level in flat space, and rely on perturbative calculations to derive interesting quantum physics
Summary
The question of how moduli come to acquire masses in the true vacuum is central in the context of string phenomenology. [7,8,9,10,11,12,13,14,15,16,17], and the question of stability was addressed in the heterotic string in [9,10,18,19,20,21,22], and more recently in the type I framework in [23,24] In all these works, supersymmetry breaking was implemented by the string versions [25,26,27,28,29,30,31,32,33,34,35,36,37] of the Scherk–Schwarz mechanism [38], with the effective potential being studied directly using string perturbation theory at one loop. Potential is extremal with respect to the open-string WL’s (see Eq (1.1)), all degrees of freedom of the internal metric are flat directions (up to exponentially suppressed terms), except the supersymmetry breaking scale M itself when nF = nB. This will prepare us for the following sections, where we consider the response of the system to the breaking of supersymmetry, in particular its one-loop stability
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