[Paper Review] The unbearable lightness of charged gravitini

Gianguido Dall’Agata, Maxim Emelin+2 more|arXiv (Cornell University)|Aug 9, 2021

Black Holes and Theoretical Physics49 references4 citations

TL;DR

This paper proves that in de Sitter vacua of N=2 gauged supergravity, charged gravitini with parametrically small or vanishing Lagrangian mass violate the magnetic weak gravity conjecture (WGC), thereby ruling out such solutions as part of the swampland. The result applies to all known stable de Sitter solutions in N=2 supergravity and extends to N=8, providing strong evidence that (quasi) de Sitter spacetimes with light charged gravitini are incompatible with quantum gravity.

ABSTRACT

We prove that charged gravitini cannot have parametrically small or vanishing Lagrangian mass in de Sitter vacua of extended supergravity while respecting the magnetic weak gravity conjecture. This places large classes of de Sitter solutions of gauged supergravity in the swampland, including all known stable solutions of the N=2 theory. We illustrate this result by analyzing a variety of de Sitter critical points of N=2 matter-coupled supergravity that also include new stable de Sitter solutions. Our results provide concrete evidence that (quasi) de Sitter with charged light gravitini should belong to the swampland, which also strongly resonates with the festina lente bound.

Motivation & Objective

• To establish that de Sitter vacua of extended supergravity with light charged gravitini are inconsistent with quantum gravity, as encoded in the magnetic weak gravity conjecture (WGC).
• To provide a general proof that parametrically light or massless charged gravitini in N=2 gauged supergravity lead to violation of the magnetic WGC.
• To extend the result to N=8 supergravity and suggest its universality for 8>N>2 extended supergravities.
• To validate the consistency of the 'festina lente' bound by showing it aligns with the WGC violation in the presence of light charged gravitini.
• To identify which known de Sitter solutions—stable or unstable—are excluded by this criterion, including those not ruled out by other swampland conjectures.

Proposed method

• Formulate the N=2 gauged supergravity framework with vector and hypermultiplets, using the coset space SO(4,2)/SO(4)×SO(2) to describe the hypermultiplet scalar manifold.
• Compute the gravitino mass and charge using the supergravity potential and the Killing spinor equation, identifying conditions under which gravitini are light and charged.
• Apply the magnetic WGC, which requires the existence of a state with charge-to-mass ratio exceeding that of a black hole, and derive the condition for its violation.
• Analyze explicit models with SO(2,1)×U(1), SO(3)×U(1), and SO(3)×O(1,1) gauge groups, including both stable and unstable de Sitter critical points.
• Use the vielbein and metric derived from the coset representative to compute the geometry of the scalar manifold and the associated Killing vectors.
• Cross-validate results using the 'festina lente' bound, which imposes a lower bound on charged particle masses in de Sitter space, showing consistency with WGC violation.

Experimental results

Research questions

• RQ1 Can de Sitter vacua of N=2 matter-coupled supergravity with light charged gravitini be consistent with the magnetic weak gravity conjecture?
• RQ2 What is the general condition under which light charged gravitini lead to violation of the magnetic WGC in de Sitter spacetime?
• RQ3 Are all known stable de Sitter solutions of N=2 supergravity excluded by this criterion?
• RQ4 How does the presence of light charged gravitini affect the UV cutoff of the effective field theory?
• RQ5 Is the 'festina lente' bound consistent with the WGC violation observed in the presence of light charged gravitini?

Key findings

• Charged gravitini with vanishing or parametrically small Lagrangian mass in de Sitter vacua of N=2 supergravity violate the magnetic weak gravity conjecture.
• All known stable de Sitter solutions of N=2 supergravity are excluded by this criterion, placing them in the swampland.
• The result extends to N=8 supergravity, indicating that such light charged gravitini are incompatible with (quasi) de Sitter spacetimes in extended supergravity.
• The violation of the magnetic WGC correlates strongly with the 'festina lente' bound, providing a non-trivial consistency check on both conjectures.
• Solutions with uncharged gravitini or broken gauge symmetry at the critical point evade exclusion, highlighting the necessity of both charge and lightness.
• The analysis identifies specific models—such as SO(2,1)×U(1) with one or two hypermultiplets—where the WGC is violated, even when other swampland criteria do not apply.