[Paper Review] The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics

Mariana Graña, Álvaro Herráez|arXiv (Cornell University)|Jun 30, 2021

Cosmology and Gravitation TheoriesPhysics and Astronomy140 references156 citations

TL;DR

This review proposes that swampland conjectures—constraints from quantum gravity—provide a bridge from quantum gravity to particle physics by restricting viable low-energy effective field theories. It demonstrates how these conjectures, particularly the Weak Gravity Conjecture, Distance Conjectures, and Festina Lente bound, lead to quantitative bounds on neutrino masses, the Higgs vacuum expectation value, the cosmological constant, and photon mass, while also constraining supersymmetry and gauge group ranks.

ABSTRACT

The swampland is the set of seemingly consistent low-energy effective field theories that cannot be consistently coupled to quantum gravity. In this review we cover some of the conjectural properties that effective theories should possess in order not to fall in the swampland, and we give an overview of their main applications to particle physics. The latter include predictions on neutrino masses, bounds on the cosmological constant, the electroweak and QCD scales, the photon mass, the Higgs potential and some insights about supersymmetry.

Motivation & Objective

• To establish a theoretical bridge between quantum gravity and particle physics using swampland conjectures.
• To investigate how quantum gravity constraints—such as the absence of global symmetries and the Weak Gravity Conjecture—impose non-trivial bounds on low-energy particle physics parameters.
• To explore the implications of swampland conjectures for unresolved problems in particle physics, including the electroweak hierarchy, neutrino masses, and the cosmological constant.
• To demonstrate that swampland constraints reduce the naive parameter space of effective field theories, offering new insights into naturalness and fine-tuning.
• To provide phenomenologically testable predictions from quantum gravity, such as upper bounds on neutrino masses and the Higgs vacuum expectation value, derived from cosmological and gravitational consistency conditions.

Proposed method

• Analyzing string theory compactifications to derive swampland constraints applicable to four-dimensional effective field theories.
• Applying the Weak Gravity Conjecture to constrain the mass of the photon and the existence of light states in U(1) gauge theories.
• Using the Distance Conjecture and its extensions (AdS and Gravitino Distance Conjectures) to predict infinite towers of light states at large field distances.
• Applying the Festina Lente bound, derived from black hole decay in de Sitter space, to constrain the Higgs potential and the electroweak scale.
• Combining cobordism conjectures with anomaly cancellation to derive allowed ranks and structures of gauge groups in four-dimensional EFTs.
• Using the Non-Susy AdS Conjecture and the refined de Sitter conjecture to constrain the stability of vacuum states and derive bounds on the Higgs and neutrino masses.

Experimental results

Research questions

• RQ1 How do swampland conjectures such as the Weak Gravity Conjecture and Distance Conjecture constrain the mass of the Higgs boson and the electroweak scale?
• RQ2 What are the implications of the non-susy AdS conjecture and the AdS Distance Conjecture for neutrino mass generation and the hierarchy problem?
• RQ3 Can the Festina Lente bound explain the smallness of the cosmological constant and the electroweak hierarchy without fine-tuning?
• RQ4 How do swampland constraints on gauge groups and global symmetries restrict viable extensions of the Standard Model?
• RQ5 To what extent do swampland conjectures unify seemingly unrelated scales in particle physics, such as the neutrino mass and the cosmological constant?

Key findings

• The non-susy AdS conjecture implies that pure Majorana neutrinos with large Majorana masses are inconsistent with quantum gravity, favoring (pseudo-)Dirac neutrinos with an upper bound on their mass of mν ≲ Λ1/4₄ ∼ 10⁻³ eV.
• Applying the Festina Lente bound to the SM U(1) gauge group reduces the discrepancy between the Planck scale and the cosmological constant to Λ₄ ≲ 10⁻⁸⁹M⁴ₚ, and forbids a local minimum at the origin of the Higgs potential without extreme fine-tuning.
• The Higgs vacuum expectation value is bounded from below by v ≳ ΛQCD ∼ 100 MeV when supersymmetry is required to stabilize lower-dimensional AdS vacua.
• The Gravitino Distance Conjecture predicts a tower of light states with scale mtower ≲ 10¹³ GeV, ruling out low-energy supersymmetry in the big desert scenario.
• The Weak Gravity Conjecture for magnetically charged strings implies that the SM photon must be exactly massless, as a finite UV cutoff below 10 MeV would otherwise be predicted.
• Cobordism conjectures combined with anomaly cancellation restrict the allowed ranks and structures of gauge groups, forbidding certain groups and relating the rank to the spacetime dimension.