[Paper Review] A Gravitino Distance Conjecture

Alberto Castellano, Anamarı́a Font+2 more|arXiv (Cornell University)|Apr 20, 2021

Black Holes and Theoretical Physics89 references18 citations

TL;DR

The paper proposes the Gravitino Distance Conjecture (GDC), asserting that in consistent supergravity with non-zero gravitino mass, the limit $ m_{3/2} \to 0 $ corresponds to infinite distance in moduli space, triggering a tower of Kaluza-Klein (KK) states and tensionless strings with mass scaling as $ M_{\text{tower}} \sim m_{3/2}^\delta $. The conjecture unifies the AdS Distance Conjecture and Swampland Distance Conjecture, with $ \delta \geq 1/3 $ for Calabi-Yau threefolds and $ \delta \geq 1/4 $ for fourfolds.

ABSTRACT

We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit $m_{3/2} ightarrow 0$ is at infinite distance. In particular one can write $M_{\mathrm{tower}} \sim m_{3/2}^δ$ 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 $ frac13 \le δ\le 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 $δ\, \geq \, \frac{1}{3}, \, \frac{1}{4}$ 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 $H \lesssim m_{3/2}^δM^{(1-δ)}_{ ext{P}}$.

Motivation & Objective

• To identify a physically privileged infinite distance limit in moduli space, distinct from arbitrary field directions.
• To establish a connection between the gravitino mass $ m_{3/2} \to 0 $ and the emergence of infinite towers of light states, including KK modes and tensionless strings.
• To unify the AdS Distance Conjecture (ADC) and the Swampland Distance Conjecture (SDC) via the GDC, with $ \delta $ as a key exponent.
• To derive lower bounds on $ \delta $ in Calabi-Yau compactifications using asymptotic Hodge theory and F-theory flux compactifications.
• To explore phenomenological implications, particularly for low-energy supersymmetry and inflation scale constraints.

Proposed method

• Propose the Gravitino Distance Conjecture (GDC) as a new distance conjecture, where $ m_{3/2} \to 0 $ implies infinite geodesic distance in moduli space.
• Use the Weak Gravity Conjecture (WGC) applied to strings and membranes to motivate the GDC, as tensionless states violate WGC unless excluded by UV completion.
• Analyze classical 4d type IIA orientifold vacua with compactifications on Calabi-Yau threefolds and F-theory on Calabi-Yau fourfolds.
• Apply asymptotic Hodge theory (MHS) to study gravitino mass limits in moduli space, particularly at codimension-two boundaries.
• Derive the scaling $ M_{\text{tower}} \sim m_{3/2}^\delta $, with $ \delta $ determined by the geometry and fluxes, and relate $ \delta $ to the SDC exponent $ \alpha $ and ADC exponent $ \lambda $.
• Compute bounds on $ \delta $: $ \delta \geq 1/3 $ for CY3, $ \delta \geq 1/4 $ for CY4, using mixed Hodge structures and flux compactifications.

Experimental results

Research questions

• RQ1 What is the physical significance of the $ m_{3/2} \to 0 $ limit in supergravity, and why is it a privileged infinite distance direction?
• RQ2 How does the GDC relate to the Swampland Distance Conjecture (SDC) and the AdS Distance Conjecture (ADC), and what is the precise relation between their exponents?
• RQ3 What are the lower bounds on the exponent $ \delta $ in the scaling $ M_{\text{tower}} \sim m_{3/2}^\delta $ for Calabi-Yau threefolds and fourfolds?
• RQ4 How does the gravitino mass behave in asymptotic limits of moduli space, particularly in toroidal and F-theory orientifold compactifications?
• RQ5 What are the phenomenological consequences of the GDC for low-energy supersymmetry and the scale of inflation?

Key findings

• The GDC is supported in type IIA orientifold vacua, where $ \delta $ ranges from $ 1/3 $ to $ 1 $, with $ \delta = 1/3 $ in AdS vacua and $ \delta = 2/3 $ in toroidal models.
• The exponent $ \delta $ satisfies $ \delta \geq 1/3 $ for Calabi-Yau threefolds and $ \delta \geq 1/4 $ for Calabi-Yau fourfolds, derived via asymptotic Hodge theory and flux compactifications.
• The GDC implies the AdS Distance Conjecture, with the ADC exponent $ \lambda = \delta / 2 $, and the SDC exponent $ \alpha $ satisfies $ \alpha / \delta = \sqrt{3/2} $ in toroidal models.
• In the $ m_{3/2} \to 0 $ limit, tensionless membranes and strings emerge, whose gauge couplings vanish, violating the WGC and supporting the singular nature of this limit.
• Phenomenologically, $ m_{3/2} \sim 1 $ TeV implies a KK scale $ M_{KK} \sim 10^8 $–$ 10^{13} $ GeV, ruling out the traditional GUT desert scenario.
• Inflation is constrained by $ H \lesssim m_{3/2}^\delta M_P^{1-\delta} $, providing an upper bound on the Hubble scale during inflation.