Abstract
We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit m3/2 → 0 is at infinite distance. In particular one can write Mtower ~ {m}_{3/2}^{delta } so that as the gravitino mass goes to zero, a tower of KK states as well as emergent strings becomes tensionless. This conjecture may be motivated from the Weak Gravity Conjecture as applied to strings and membranes and implies in turn the AdS Distance Conjecture. We test this proposal in classical 4d type IIA orientifold vacua in which one obtains a range of values frac{1}{3} ≤ δ ≤ 1. The parameter δ is related to the scale decoupling exponent in AdS vacua and to the α exponent in the Swampland Distance Conjecture for the type IIA complex structure. We present a general analysis of the gravitino mass in the limits of moduli space in terms of limiting Mixed Hodge Structures and study in some detail the case of two-moduli F-theory settings. Moreover, we obtain general lower bounds δ ≥ frac{1}{3},frac{1}{4} for Calabi-Yau threefolds and fourfolds, respectively. The conjecture has important phenomenological implications. In particular we argue that low-energy supersymmetry of order 1 TeV is only obtained if there is a tower of KK states at an intermediate scale, of order 108 GeV. One also has an upper bound for the Hubble constant upon inflation H ≲ {m}_{3/2}^{delta }{M}_{mathrm{P}}^{left(1-delta right)} .
Highlights
We present a general analysis of the gravitino mass in the limits of moduli space in terms of limiting Mixed Hodge Structures and study in some detail the case of two-moduli F-theory settings
Well understood semiclassical properties of black holes. These general properties are often stated in terms of Swampland Conjectures which try to capture essential properties coming from Quantum Gravity (QG)
In particular we argue that the limit m3/2 → 0 in quantum gravity is at infinite distance
Summary
In order to set the stage, we review the Swampland Distance Conjecture (SDC) [6] and the Anti-de Sitter Distance Conjecture (ADC) [24], as they turn to be closely related to our Gravitino Distance Conjecture (GDC), that we present . It is clear that even though the breakdown of gravitational EFTs by the appearance of light towers of states seems to be ubiquitous in String Theory, this generality makes it harder to pinpoint the towers that could be more relevant for connecting this to our Universe In this regard, we will focus in this article on a particular limit, namely the one associated with the gravitino mass going to zero. One could say that the Gravitino Distance Conjecture, that we present, allows us to unify the SDC and the ADC when the special limits selected by the vanishing of the gravitino mass are considered In this sense, are we adding one conjecture to the already rich web of Swampland Conjectures, and connecting it to some of the existing ones as well as recovering non-trivial results for the bounds on their parameters [11,12,13], as we will explain later
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