[Paper Review] String (In)Stability Issues with Broken Supersymmetry

J. Mourad, Augusto Sagnotti|arXiv (Cornell University)|Jul 8, 2021

Cosmology and Gravitation Theories19 references4 citations

TL;DR

This paper investigates string compactifications with broken supersymmetry, showing that tadpole potentials in weakly-coupled type IIB string theory can drive cosmological solutions with early-time fast-roll inflation and spontaneous compactification to lower-dimensional Minkowski space. Despite instabilities from internal fluxes, perturbative stability is preserved when flux scale $ h \gtrsim 1 $ and compactification radius $ R/\rho \lesssim 10^{-2} $, suggesting viable, stable compactifications without full supersymmetry.

ABSTRACT

We review the main results of our investigations motivated by the tadpole potentials of ten-dimensional strings with broken supersymmetry. While these are at best partial indications, it is hard to resist the feeling that they do capture some lessons of String Theory. For example, these very tadpole potentials lead to weak-string-coupling cosmologies that appear to provide clues on the onset of the inflation from an initial fast roll. The transition, if accessible to us, would offer a natural explanation for the lack of power manifested by the CMB at large angular scales. In addition, the same tadpole potentials can drive spontaneous compactifications to lower-dimensional Minkowski spaces at corresponding length scales. Furthermore, the cosmological solutions exhibit an intriguing "instability of isotropy" that, if taken at face value, would point to an accidental origin of compactification. Finally, symmetric static AdS x S solutions driven by the tadpole potentials also exist, but they are unstable due to mixings induced by their internal fluxes. On the other hand, the original Dudas-Mourad solution is perturbatively stable, and we have gathered some detailed evidence that instabilities induced by internal fluxes can be held under control in a similar class of weak-coupling type-IIB compactifications to Minkowski space.

Motivation & Objective

• To investigate the stability and cosmological implications of string compactifications with broken supersymmetry, particularly in the context of tadpole potentials.
• To assess whether weakly-coupled type IIB string theories with broken supersymmetry can yield viable cosmological solutions and stable Minkowski compactifications.
• To analyze the role of internal fluxes in inducing instabilities and determine conditions under which perturbative stability can be preserved.
• To explore the possibility of spontaneous compactification to lower-dimensional Minkowski spacetime driven by tadpole potentials.
• To evaluate the viability of non-symmetric internal spaces for stable, low-energy effective field theories in broken supersymmetry scenarios.

Proposed method

• Analyzes tadpole potentials in ten-dimensional string theories with broken supersymmetry, focusing on their cosmological and compactification implications.
• Uses analytic continuation to map Lorentzian cosmological solutions to Euclidean Schrödinger-type problems for stability analysis.
• Applies variational techniques to study scalar perturbations with non-zero Kaluza–Klein momentum $ \mathbf{k} \neq 0 $, particularly in fluxed compactifications.
• Introduces a dimensionless flux parameter $ h = |H_5|\rho / \sqrt{2} $ to characterize the scale of five-form field strength and its impact on stability.
• Examines the spectrum of singlet scalar perturbations, identifying non-symmetric Schrödinger potentials that may yield complex eigenvalues signaling instabilities.
• Derives the condition $ R/\rho < \eta_c \sim 10^{-2} $ for stability, ensuring effective field theory reliability when $ \rho \sim (10^4 - 10^5)\sqrt{\alpha'} $.

Experimental results

Research questions

• RQ1 Can tadpole potentials in weakly-coupled type IIB string theories lead to cosmological solutions with early-time fast-roll inflation?
• RQ2 Under what conditions can broken supersymmetry in string compactifications yield stable, low-energy Minkowski vacua?
• RQ3 How do internal fluxes affect the stability of scalar perturbations in compactified string models?
• RQ4 Can non-symmetric internal spaces support stable compactifications in the absence of full supersymmetry?
• RQ5 What role does the flux scale $ h $ play in suppressing instabilities from complex eigenvalues in the scalar spectrum?

Key findings

• Tadpole potentials in broken supersymmetry scenarios lead to cosmological solutions with early-time fast-roll inflation, potentially explaining the low CMB power at large angular scales.
• Spontaneous compactification to lower-dimensional Minkowski spaces is driven by the same tadpole potentials, suggesting a dynamical origin for compactification scales.
• The system exhibits an 'instability of isotropy' that may point to an accidental origin of compactification, challenging conventional symmetry-based explanations.
• Symmetric $AdS \times S$ solutions exist but are unstable due to flux-induced mixings, while the original Dudas–Mourad solution remains perturbatively stable.
• For $ h \gtrsim 1 $, complex eigenvalues—indicating dangerous instabilities—disappear, and the system passes all perturbative stability tests.
• Stability is ensured when $ R/\rho < \eta_c \sim 10^{-2} $, with $ \rho \sim (10^4 - 10^5)\sqrt{\alpha'} $, validating the effective field theory description.