The Swampland Conjectures: A bridge from Quantum Gravity to Particle Physics

TL;DR

This review surveys the swampland program, detailing conjectures that distinguish EFTs compatible with quantum gravity from those that are not, and then translates these constraints into particle-physics implications. By examining global-symmetry absence, the Weak Gravity Conjecture, distance/tower conjectures, and cobordism reasoning, the authors derive concrete bounds on neutrino masses, the cosmological constant, the electroweak scale, photon mass, and gauge-group structures. Key results include $m_\nu \lesssim \Lambda_4^{1/4}$ for Dirac neutrinos, the Festina Lente bound linking charged-particle spectra to $H$-driven dS backgrounds, and arguments favoring SUSY completions to stabilize certain compactifications; they also argue for a strictly massless photon via axion/1-form WGC logic. Collectively, these connections suggest a reimagined naturalness paradigm where quantum gravity dictates relationships among seemingly disparate SM parameters, offering a bridge between UV consistency and phenomenology with potential guidance for future model-building.

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.

Figures (7)

• Figure 1: (a) Two cobordant $d$-dimensional manifolds, which at the level of a lower dimensional EFT give rise to a domain wall separating a theory compactified on both of them. (a) A $d$-dimensional manifold in the trivial cobordism class. Compactifying a theory in such a manifold thus supports an end of the world membrane separating it from nothing.
• Figure 2: (a) Shift in a flux $f_0$ as a consequence of crossing a membrane with charge $q$ under the dual 3-form. (b) Vacuum decay by nucleation of a bubble that expands and is surrounded by a membrane with charge $q$, such that the flux outside the bubble, $f_0$, is reduced in the internal region of the bubble.
• Figure 3: (a) Illustration of an extra circular dimension, the $x$-direction represents the non-compact space. (b) If the size of the extra dimension (i.e. the circle) is reduced along the non-compact direction until it eventually reaches zero size, a region of space is removed (the one that corresponds to the values of $x$ that are between the two black dots). (c) A bubble of nothing in more dimensions is obtained when the size of the extra dimension becomes zero at the boundary of such a region. Here we have represented this schematically only at two points in the boundary of the bubble, but in reality there would be one cigar-like blue figure attached to each point on the boundary of the bubble.
• Figure 4: Figs. taken from Montero:2019ekk. (a) Phase space of Reissner-Nordström-de Sitter black holes. (b)Decay of Nariai black holes by emission of particles with $m^2\ll qE$, so that they discharge almost instantaneously without effectively loosing mass.
• Figure 5: Figs. taken from Gonzalo:2018tpb. The vertical axis represents the 3d effective potential for the radion, $V(R)$ (in units of with $r=1$GeV), multiplied times $R^6$ so as to give a constant profile when $R\rightarrow 0$, and it is normalized by the contribution of one degree of freedom (a) Radion effective potential for Majorana neutrinos (with heavy Majorana masses) where an AdS minimum always develops. (b) Radion effective potential for (pseudo-)Dirac neutrinos with different values for the lightest neutrino mass $m_{\nu_1}$ (in mili-electron volts). The formation of an AdS vacuum can be avoided if the neutrino masses are light enough.