Leaving the Swampland: non-geometric fluxes and the distance conjecture

Abstract

We study a Type IIB isotropic toroidal compactification with non-geometric fluxes. Under the assumption of a hierarchy on the moduli, an effective scalar potential is constructed showing a runaway direction on the real part of the Kähler modulus while the rest of the moduli are stabilized. For the effective model to be consistent it is required that displacements in the field space are finite. Infinite distances in field space would imply a breakdown in the hierarchy assumption on the moduli. In this context, the Swampland Distance Conjecture is satisfied suggesting the possibility of leaving or entering the Swampland by a parametric control of the fluxes. This is achieved upon allowing the non-geometric fluxes to take fractional values. In the process we are able to compute the cut-off scale below which the theory is valid, completely depending on the flux configuration. We also report on the appearance of a discrete spectrum of values for the string coupling at the level of the effective theory.

Testing swampland conjectures with machine learning

“…Hence we can expect a small value for |V min | if ω and |P 2 | at U = U 0 are also smaller than one. As shown in [44], ω ∼ O(1) in flux units. This implies that…”

“…A hierarchy on the integer values associated to all fluxes in turn establishes a hierarchy on the masses associated to the modulus. This is, if we take for example the R-R fluxes to be larger than the others f h, b, we expect in this model, that the complex structure modulus would be the heaviest modulus M U M S , M T [44]. Next we write the expected hierarchies between the moduli masses that are obtained by setting one of the explored hierarchies among the fluxes:…”

“…while s is kept unfixed. We shall fix it by minimizing the scalar potential with respect to s. However, as shown in [44], roots U 0 for the above polynomial implies that P 3 (U 0 ) = 0. In order to keep a SUSY solution we shall then assume that lim which by taking same order fluxes among the same type of fluxes (e.g., all RR fluxes are the same order but larger than all NS-NS, which are of the same order among them), one can assure that Im(P 2 (U 0 )ω * (U 0 )) be smaller than unit.…”

“…Based on recent results [13,25,44], in which the presence of hierarchical values on fluxes induces a natural hierarchy on moduli masses, for which there are concrete (supersym-metric and non-supersymmetric) vacuum solutions with a small value for the cosmological constant Λ, we contemplate the possibility that hierarchical flux configurations lead to scenarios with small values for the vacuum energy. We observe that indeed, the values of the scalar potential at its minimum are smaller than one when the flux configuration possesses a hierarchy among their integer values.…”

“…More constraints would involve a sharing solution with a similar equation for P 1 (U ). See Ref [44]…”