Swampland criteria like the Weak Gravity Conjecture should not only apply to particles, but also to other lower-codimension charged objects in 4d EFTs like strings and membranes. However, the description of the latter is in general subtle due to their large backreaction effects. In the context of 4d $$ \mathcal{N} $$
 = 1 EFTs, we consider $$ \frac{1}{2} $$
 BPS strings and membranes which are fundamental, in the sense that they cannot be resolved within the EFT regime. We argue that, if interpreted from the EFT viewpoint, the 4d backreaction of these objects translates into a classical RG flow of their couplings. Constraints on the UV charges and tensions get then translated to constraints on the axionic kinetic terms and scalar potential of the EFT. This uncovers new relations among the Swampland Conjectures, which become interconnected by the physical properties of low-codimension objects. In particular, using that string RG flows describe infinite field distance limits, we show that the WGC for strings implies the Swampland Distance Conjecture. Similarly, WGC-saturating membranes generate a scalar potential satisfying the de Sitter Conjecture.

/pdf/swampland-conjectures-for-strings-and-membranes-1oj8c20212.pdf

Swampland Conjectures for strings and membranes

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.

https://www.mdpi.com/2218-1997/7/8/273/pdf

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

We study quantum corrections in four-dimensional theories with N = 1 supersymmetry in the context of Quantum Gravity Conjectures. According to the Emergent String Conjecture, infinite distance limits in quantum gravity either lead to decompactification of the theory or result in a weakly coupled string theory. We verify this conjecture in the framework of N = 1 supersymmetric F-theory compactifications to four dimensions including perturbative α′ as well as non-perturbative corrections. After proving uniqueness of the emergent critical string at the classical level, we show that quantum corrections obstruct precisely those limits in which the scale of the emergent critical string would lie parametrically below the Kaluza-Klein scale. Limits in which the tension of the asymptotically tensionless string sits at the Kaluza-Klein scale, by contrast, are not obstructed. In the second part of the paper we study the effect of quantum corrections for the Weak Gravity Conjecture away from the strict weak coupling limit. We propose that gauge threshold corrections and mass renormalisation effects modify the super-extremality bound in four dimensions. For the infinite distance limits in F-theory the classical super-extremality bound is generically satisfied by a sublattice of states in the tower of excitations of an emergent heterotic string. By matching the F-theory α′-corrections to gauge threshold corrections of the dual heterotic theory we predict how the masses of this tower must be renormalised in order for the Weak Gravity Conjecture to hold at the quantum level.

/pdf/quantum-corrections-in-4d-n-1-infinite-distance-limits-and-14863irxey.pdf

Quantum corrections in 4d N = 1 infinite distance limits and the weak gravity conjecture

We propose a new swampland conjecture stating that the limit of vanishing gravitino mass corresponds to the massless limit of an infinite tower of states and to the consequent breakdown of the effective field theory. We test our proposal in large classes of models coming from compactification of string theory to four dimensions, where we identify the Kaluza-Klein nature of the tower of states becoming light. We point out a general relation between the gravitino mass and abelian gauge coupling in models with extended supersymmetry, which can survive also in examples with minimal supersymmetry. This allows us to connect our conjecture to other well established swampland conjectures, such as the weak gravity conjecture or the absence of global symmetries in quantum gravity. We discuss phenomenological implications of our conjecture in (quasi-)de Sitter backgrounds and extract a lower bound for the gravitino mass in terms of the Hubble parameter.

/pdf/the-gravitino-and-the-swampland-56qxj3ekmz.pdf

The gravitino and the swampland

Demanding that charged Nariai black holes in (quasi-)de Sitter space decay without becoming super-extremal implies a lower bound on the masses of charged particles, known as the Festina Lente (FL) bound. In this paper we fix the $$ \mathcal{O}(1) $$
 constant in the bound and elucidate various aspects of it, as well as extensions to d > 4 and to situations with scalar potentials and dilatonic couplings. We also discuss phenomenological implications of FL including an explanation of why the Higgs potential cannot have a local minimum at the origin, thus explaining why the weak force must be broken. For constructions of meta-stable dS involving anti-brane uplift scenarios, even though the throat region is consistent with FL, the bound implies that we cannot have any light charged matter fields coming from any far away region in the compactified geometry, contrary to the fact that they are typically expected to arise in these scenarios. This strongly suggests that introduction of warped anti-branes in the throat cannot be decoupled from the bulk dynamics as is commonly assumed. Finally, we provide some evidence that in certain situations the FL bound can have implications even with gravity decoupled and illustrate this in the context of non-compact throats.

/pdf/the-fl-bound-and-its-phenomenological-implications-3hl4z8lerc.pdf

The FL bound and its phenomenological implications

We analyze the charge-to-mass structure of BPS states in general infinite-distance limits of $$ \mathcal{N} $$
 = 2 compactifications of Type IIB string theory on Calabi-Yau three-folds, and use the results to sharpen the formulation of the Swampland Conjectures in the presence of multiple gauge and scalar fields. We show that the BPS bound coincides with the black hole extremality bound in these infinite distance limits, and that the charge-to-mass vectors of the BPS states lie on degenerate ellipsoids with only two non-degenerate directions, regardless of the number of moduli or gauge fields. We provide the numerical value of the principal radii of the ellipsoid in terms of the classification of the singularity that is being approached. We use these findings to inform the Swampland Distance Conjecture, which states that a tower of states becomes exponentially light along geodesic trajectories towards infinite field distance. We place general bounds on the mass decay rate λ of this tower in terms of the black hole extremality bound, which in our setup implies $$ \lambda \ge 1/\sqrt{6} $$
 . We expect this framework to persist beyond $$ \mathcal{N} $$
 = 2 as long as a gauge coupling becomes small in the infinite field distance limit.

/pdf/merging-the-weak-gravity-and-distance-conjectures-using-bps-yt6zhxwcsa.pdf

Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes

We analyze the charge-to-mass structure of BPS states in general infinite-distance limits of $\mathcal{N}=2$ compactifications of Type IIB string theory on Calabi-Yau three-folds, and use the results to sharpen the formulation of the Swampland Conjectures in the presence of multiple gauge and scalar fields. We show that the BPS bound coincides with the black hole extremality bound in these infinite distance limits, and that the charge-to-mass vectors of the BPS states lie on degenerate ellipsoids with only two non-degenerate directions, regardless of the number of moduli or gauge fields. We provide the numerical value of the principal radii of the ellipsoid in terms of the classification of the singularity that is being approached. We use these findings to inform the Swampland Distance Conjecture, which states that a tower of states becomes exponentially light along geodesic trajectories towards infinite field distance. We place general bounds on the mass decay rate $\lambda$ of this tower in terms of the black hole extremality bound, which in our setup implies $\lambda \geq 1/\sqrt{6}$. We expect this framework to persist beyond $\mathcal{N}=2$ as long as a gauge coupling becomes small in the infinite field distance limit.

/pdf/merging-the-weak-gravity-and-distance-conjectures-using-bps-5a0k2hxuf1.pdf

https://link.springer.com/content/pdf/10.1007/JHEP11(2022)142.pdf

Superpotentials from singular divisors

We present a method to construct the extended Kähler cone of any Calabi-Yau threefold by using Gopakumar-Vafa invariants to identify all geometric phases that are related by flops or Weyl reflections. In this way we obtain the Kähler moduli spaces of all favorable Calabi-Yau threefold hypersurfaces with h ≤ 4, including toric and non-toric phases. In this setting we perform an explicit test of the Weak Gravity Conjecture by using the Gopakumar-Vafa invariants to count BPS states. All of our examples satisfy the tower/sublattice WGC, and in fact they even satisfy the stronger lattice WGC. ar X iv :2 21 2. 10 57 3v 1 [ he pth ] 2 0 D ec 2 02 2

Naomi Gendler

Papers

Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes

Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes

Superpotentials from singular divisors

Moduli Space Reconstruction and Weak Gravity