A Gravitino Distance Conjecture

Abstract

We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit $m_{3/2}\to 0$ is at infinite distance. In particular one can write $M_{\mathrm{tower}}\sim m_{3/2}^{\delta }$ 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 $\frac{1}{3}\le \delta \le 1$. The parameter $\delta$ is related to the scale decoupling exponent in AdS vacua and to the $\alpha$ 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 $\delta \ge \frac{1}{3},\frac{1}{4}$ 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 $10^8$ GeV. One also has an upper bound for the Hubble constant upon inflation $H\lesssim m_{3/2}^{\delta }{M}_{\text{P}}^{(1-\delta )}$.

arXiv commentv2: 60 pages, 3 figures. Minor changes and references added

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• Physics of Infinite Complex Structure Limits in eight Dimensions
• Swampland dS conjecture in Mimetic $f(R,T)$ gravity
• Revisiting Dudas-Mourad compactifications
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• Quantum gravity constraints on scale separation and de Sitter in five dimensions
• Geometry of orientifold vacua and supersymmetry breaking
• Gravitino Thermal Production, Dark Matter, and Reheating of the Universe
• Uplift and towers of states in warped throat
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
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