A gravitino distance conjecture

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 ~ $$ {m}_{3/2}^{\delta } $$ m 3 / 2 δ 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 $$ \frac{1}{3} $$ 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 ≥$$ \frac{1}{3},\frac{1}{4} $$ 1 3 , 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 ≲ $$ {m}_{3/2}^{\delta }{M}_{\mathrm{P}}^{\left(1-\delta \right)} $$ m 3 / 2 δ M P 1 − δ .

Geometry of orientifold vacua and supersymmetry breaking

Starting from a peculiar orientifold projection proposed long ago by Angelantonj and Cardella, we elaborate on a novel perturbative scenario that involves only D-branes, together with the two types of orientifold planes O± and anti-orientifold planes $$ {\overline{\mathrm{O}}}_{\pm } $$ O ¯ ± . We elucidate the microscopic ingredients of such models, connecting them to a novel realization of brane supersymmetry breaking. Depending on the position of the D-branes in the internal space, supersymmetry can be broken at the string scale on branes, or alternatively only at the massive level. The main novelty of this construction is that it features no NS-NS disk tadpoles, while avoiding open-string instabilities. The one-loop potential, which depends on the positions of the D-branes, is minimized for maximally broken, non-linearly realized supersymmetry. The orientifold projection and the effective field theory description reveal a soft breaking of supersymmetry in the closed-string sector. In such models it is possible to decouple the gravitino mass from the value of the scalar potential, while avoiding brane instabilities.

The gravitino and the swampland

We propose a new swampland conjecture stating that the limit of vanishing gravitino mass corresponds to the massless limit of an infinite tower of states and to the consequent breakdown of the effective field theory. We test our proposal in large classes of models coming from compactification of string theory to four dimensions, where we identify the Kaluza-Klein nature of the tower of states becoming light. We point out a general relation between the gravitino mass and abelian gauge coupling in models with extended supersymmetry, which can survive also in examples with minimal supersymmetry. This allows us to connect our conjecture to other well established swampland conjectures, such as the weak gravity conjecture or the absence of global symmetries in quantum gravity. We discuss phenomenological implications of our conjecture in (quasi-)de Sitter backgrounds and extract a lower bound for the gravitino mass in terms of the Hubble parameter.

Charms of strongly interacting conformal gauge mediation

By extending a previously proposed conformal gauge mediation model, we construct a gauge-mediated SUSY breaking (GMSB) model where a SUSY-breaking scale, a messenger mass, the μ-parameter and the gravitino mass in a minimal supersymmetric (SUSY) Standard Model (MSSM) are all explained by a single mass scale, a R-symmetry breaking scale. We focus on a low scale SUSY-breaking scenario with the gravitino mass m3/2 = $$ \mathcal{O}(1)\mathrm{eV} $$ O 1 eV , which is free from the cosmological gravitino problem and relaxes the fine-tuning of the cosmological constant. Both the messenger and SUSY-breaking sectors are subject to a hidden strong dynamics with the conformality above the messenger mass threshold (and hence the name of the model “strongly interacting conformal gauge mediation”). In our model, the Higgs B-term is suppressed and a large tan β is predicted, resulting in the relatively light second CP-even Higgs and the CP-odd Higgs with a sizable production cross section. These Higgs bosons can be tested at future LHC experiments.

The upper bound of the second Higgs boson mass in minimal gauge mediation with the gravitino warm dark matter

A keV-scale gravitino arising from a minimal supersymmetric (SUSY) Standard Model (MSSM) is an interesting possibility since the small scale problems that the ΛCDM model encounters in the modern cosmology could be alleviated with the keV-scale gravitino serving as the warm dark matter (WDM). Such a light gravitino asks for a low scale supersymmetry (SUSY) breaking for which the gauge mediation (GM) is required as a consistent SUSY-breaking mediation mechanism. In this paper, we show upper bounds of the masses of the second CP-even Higgs boson H and the CP-odd Higgs boson A, assuming the keV-scale gravitino to be responsible for the current DM relic abundance: the upper bound on the mass of H/A is found to be ∼ 4 TeV for the gravitino mass of $$ \mathcal{O}\left(10-100\right) $$ O 10 − 100 keV. Interestingly, the mass of H/A can be as small as 2–3 TeV and the predicted tan β is as large as 55–60 for the gravitino mass of $$ \mathcal{O}(10) $$ O 10 keV. This will be tested in the near future Large Hadron Collider (LHC) experiments.

New Kähler invariant Fayet–Iliopoulos terms in supergravity and cosmological applications

Recently, a new type of constant Fayet–Iliopoulos (FI) terms was introduced in $${\mathcal {N}}=1$$ N = 1 supergravity, which do not require the gauging of the R-symmetry. We revisit and generalise these constructions, building a new class of Kähler invariant FI terms parametrised by a function of the gravitino mass as functional of the chiral superfields, which is then used to describe new models of inflation. They are based on a no-scale supergravity model of the inflaton chiral multiplet, supplemented by an abelian vector multiplet with the new FI-term. We show that the inflaton potential is compatible with the CMB observational data, with a vacuum energy at the minimum that can be tuned to a tiny positive value. Finally, the axionic shift symmetry can be gauged by the U(1) which becomes massive. These models offer a mechanism for fixing the gravitino mass in no-scale supergravities, that corresponds to a flat direction of the scalar potential in the absence of the new FI-term; its origin in string theory is an interesting open problem.