We propose a version of the Weak Gravity Conjecture that applies to AdS spacetime. We find that the condition on the charge-to-mass ratio of a charged particle in AdS spacetime is corrected compared to the one in Minkowski spacetime by contributions that depends on the AdS scale and the horizon radius of the extremal Reissner-Nordström black hole charged under the same gauge theory. It is maximized when we consider the largest possible extremal black hole in AdS. We motivate our proposal from the viewpoint of extremal black hole decay and show that the bound on the particle spectrum is given by the critical charge-to-mass ratio beyond which the Schwinger effect can take place. This quantum effect shares the same condition as requiring a particle to satisfy a repulsive force condition at the black hole horizon, so that the extremal black hole can decay without reabsorbing the particle. We discuss the relation of our proposed weak gravity bound with the near-horizon Breitenlohner-Freedman bound. We also comment on the generalization in the case of multiple U(1) gauge theories, providing evidence for a convex hull condition in AdS background.

United States

Puxin Lin

Alessandro Mininno

Gary Shiu

Formulating the Weak Gravity Conjecture in AdS space

The Schwinger effect has a variety of physics applications. In the context of black hole physics, it provides a channel for the decay of charged black holes. While the Schwinger rate has been derived for extremal Reissner-Nordström (RN) black hole using the $\textit{AdS}$ × $\textit{S}$ geometry of the horizon, a full analysis in the whole geometry is lacking, begging the question of whether it is sufficient to ignore contributions away from the horizon. In this paper, we address this problem and obtain the spatial profile of the Schwinger production rate in an asymptotically flat RN black hole spacetime. We find that the Schwinger effect is strongest on the horizon and decays with distance from the horizon, exhibiting a characteristic scale of the Compton wavelength of the particle. The rate is switched off when the particle’s charge-to-mass ratio approaches the corresponding extremality bound for black holes, in accordance with a strong form of the Weak Gravity Conjecture (WGC).

Schwinger effect of extremal Reissner-Nordström black holes

The cosmological dynamics of multiple scalar/pseudoscalar fields are difficult to solve, especially when the field-space metric is curved. This presents a challenge in determining whether a given model can support cosmic acceleration, without solving for the on-shell solution. In this work, we present bounds on late-time FLRW-cosmologies in classes of theories that involve arbitrary numbers of scalar and pseudoscalar fields coupled both kinetically (leading to a curved field space metric) and through scalar potentials. Such bounds are proven analytically, independently of initial conditions, with no approximation in the field equations and without referring to explicit solutions. Besides their broad applications to cosmological model building, our bounds can be applied to studying asymptotic cosmologies of certain classes of string compactifications.

Belgium

Flavio Tonioni

Hung Tran

Analytic bounds on late-time axion-scalar cosmologies

We show how flux vacua that differ from each other in flux quanta can be seen as different vacua in a single scalar potential of an enlarged field space, which resolves the separation by thin domain walls. This observation, which is motivated by the anti–de Sitter distance conjecture, allows one to compute distances between different vacua using the usual field-space metric. We verify for explicit examples such as scale-separated IIA flux vacua and the IIB Freund-Rubin vacua that the distance conjecture (for scalar fields) is satisfied and that the asymptotic directions in the enlarged field space are indeed hyperbolic. This enlarged field space contains the tachyon fields on the unstable <math><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>˜</mo></mrow></mover><mi>p</mi></mrow></math>-branes of type II string theory, which can induce the brane charges of the stable D-branes. We suggest that requiring continuous interpolations refines the cobordism conjecture and postdicts the existence of unstable <math><mover><mi>D</mi><mo>˜</mo></mover><mi>p</mi></math>-branes.

Sweden

Vincent Van Hemelryck

Thomas Van Riet

Connecting flux vacua through scalar field excursions

We prove the conditions under which scaling cosmologies are inevitable late-time attractors of multifield multiexponential potentials, independently of initial conditions. The advantage of such scaling cosmologies is that the time dependence of the fields and of the scale factor is known analytically, thus allowing late-time observables to be determined exactly. Expanding our earlier results, here we continue the program of analytically characterizing the late-time behavior of cosmological solutions. Our results are general in that they are derived without relying on any approximation nor are they based on any assumption on the sources of the potential, such as their higher-dimensional or string-theoretic origin. We point out a number of model-independent features that follow from our analytic results, including a convex-hull criterion for cosmic acceleration. When applied to string theory, our analytic knowledge of late-time cosmological solutions enables us to single out potentials that can describe an accelerating universe from those which cannot and to quantitatively test several conjectured swampland criteria.

Hung V. Tran

Late-time attractors and cosmic acceleration

We investigate whether an accelerating universe can be realized as an asymptotic late-time solution of Friedmann–Lemaître–Robertson–Walker (FLRW)-cosmology with multifield multiexponential potentials. Late-time cosmological solutions exhibit a universal behavior which enables us to bound the rate of time variation of the Hubble parameter. In string-theoretic realizations, if the dilaton remains a rolling field, our bound singles out a tension in achieving asymptotic late-time cosmic acceleration. Our findings go beyond previous no-go theorems in that they apply to arbitrary multiexponential potentials and make no specific reference to vacuum or slow-roll solutions. We also show that if the late-time solution approaches a critical point of the dynamical system governing the cosmological evolution, the criterion for cosmic acceleration can be generally stated in terms of a directional derivative of the potential.

Accelerating universe at the end of time

Euclidean wormhole geometries sourced by axions and dilatons are puzzling objects in quantum gravity. From one side of the wormhole to the other, the scalar fields traverse a few Planck lengths in field space and so corrections from the UV might potentially affect the consistency of the solution, even when the wormholes are large. Motivated by this, we carry out the first explicit 10d lifts of regular Euclidean axion wormholes. We start off with the lift of Giddings-Strominger wormholes in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 Euclidean supergravity over a 6-torus to 10d type IIA supergravity and find the solution can be everywhere tuned into the parametrically controlled supergravity regime. Secondly, we construct explicit wormholes in AdS spaces and find them again to be under parametric control. We find the first wormhole solutions in massive type IIA on S 3 × S 3 and in type IIB on T 1,1. The latter has an explicit holographic dual, and similar to the earlier constructions in AdS5 × S 5/ℤ k , the wormholes violate operator positivity since Tr(F ± ⋆ F)2 &lt; 0. This puzzle might arise from subtleties related to computing holographic n-point functions in the presence of multiple boundaries.

Japan

Gregory Loges

Thomas Riet

A 10d construction of Euclidean axion wormholes in flat and AdS space

It has been argued that orientifold vacua with fluxes in type IIA string theory can achieve moduli stabilisation and arbitrary decoupling between the AdS and KK scales upon sending certain unconstrained RR-flux quanta to infinity. In this paper, we find a novel scalar field in the open-string sector that allows us to interpolate between such IIA vacua that differ in flux quanta and find that the limit of large fluxes is nicely consistent with the distance conjecture. This shows that the massive IIA vacua pass an important Swampland criterion and suggests that scale-separated AdS vacua might not be in the Swampland. Our analysis also naturally suggests a flux analogue of “Reid’s fantasy” where flux vacua that differ in quantised flux numbers can be connected through trajectories in open-string field space and not just via singular domain walls.

Vincent Hemelryck

AdS scale separation and the distance conjecture

The landscape of string vacua is very large, but generally expected to be finite in size. Enumerating the number and properties of the vacua is an important task for both the landscape and the swampland, in part to gain a deeper understanding of what is possible and “generic”. We obtain an exact counting of distinct intersecting brane vacua of type IIA string theory on the 𝕋6 /ℤ2 × ℤ2 orientifold. Care is taken to only count gauge-inequivalent brane configurations. Leveraging the recursive nature by which branes may be added together one-by-one, we use dynamic programming to efficiently count the number of solutions of the tadpole, K-theory and supersymmetry consistency conditions. The distributions of 4D gauge group rank and complex structure moduli for the entire ensemble of intersecting brane vacua are presented. The methods we developed here may be useful in obtaining sharp upper and lower bounds on other corners of the landscape.

134 billion intersecting brane models

The mild form of the Weak Gravity Conjecture (WGC) requires higher derivative corrections to extremal charged black holes to increase their charge-to-mass ratio. This allows decay via emission of a smaller extremal black hole. In this paper, we investigate if similar constraints hold for extremal rotating black holes. We do so by considering the leading higher derivative corrections to the four-dimensional Kerr black hole and five-dimensional Myers-Perry black hole. We use a known mapping of these rotating solutions to a four-dimensional non-rotating dyonic Kaluza-Klein black hole and impose the WGC on this charged solution. Going back again to the rotating solutions, this fixes the sign of the corrections to the rotating extremality bounds. The sign of the corrections is non-universal, depending on the black hole under consideration. We argue that this is not at odds with black hole decay, because of the presence of a superradiant instability that persists in the extremal limit. When this instability is present, the WGC is implied for the four-dimensional charged black hole.