Abstract
We consider Type IIB compactifications on an isotropic torus T^6 threaded by geometric and non geometric fluxes. For this particular setup we apply supervised machine learning techniques, namely an artificial neural network coupled to a genetic algorithm, in order to obtain more than sixty thousand flux configurations yielding to a scalar potential with at least one critical point. We observe that both stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the refined de Sitter conjecture. Moreover, by considering a hierarchy among fluxes, we observe that perturbative solutions with small values for the vacuum energy and moduli masses are favored, as well as scenarios in which the lightest modulus mass is much smaller than the corresponding AdS vacuum scale. Finally we apply some results on random matrix theory to conclude that the most probable mass spectrum derived from this string setup is that satisfying the Refined de Sitter and AdS scale conjectures.
Highlights
In this context, one would be tracing back the origin of a small Λ to some well-identified features of flux configurations
In this work we focus on the so-called refined de Sitter conjecture (RdSC) which states that the construction of a stable dS vacuum is excluded from a consistent quantum gravity theory
The training consists on feeding the artificial neural network1 (ANN) with different flux configurations for which we know the existence of critical points as well as their corresponding features, such as vacuum stability and the value of the scalar potential at the critical point
Summary
One would be tracing back the origin of a small Λ to some well-identified features of flux configurations. The values of the scalar potential at its minimum are smaller than one when the flux configuration possesses a hierarchy among their integer values In this sense we suggest that a possible microscopic explanation for a small Λ in a quantum gravity theory such as string theory, might rely on specific features of the flux configuration. All generated vacua seems to satisfy the RdS conjecture we find that by restricting the construction of these simple models to hierarchical flux configurations, we increase the probability for the effective models to be in the perturbative regime and to fulfill scale conjecture as well This suggests, at least for these simple toroidal models, that the source of the Swampland constraints could rely on specific features of flux configurations as the hierarchical values among them. A toy example illustrating the possibility to have small vacuum energy values at an extremum of the scalar potential is presented in Appendix B as well
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