Swampland Constraints Research Articles

Dynamical tadpoles and Weak Gravity Constraints

Non-supersymmetric string models are plagued with tadpoles for dynamical fields, which signal uncanceled forces sourced by the vacuum. We argue that in certain cases, uncanceled dynamical tadpoles can lead to inconsistencies with quantum gravity, via violation of swampland constraints. We describe an explicit realization in a supersymmetric toroidal Z2 × Z2 orientifold with D7-branes, where the dynamical tadpole generated by displacement of the D7-branes off its minimum leads to violation of the axion Weak Gravity Conjecture. In these examples, cancellation of dynamical tadpoles provides consistency conditions for the configuration, of dynamical nature (as opposed to the topological conditions of topological tadpoles, such as RR tadpole cancellation in compact spaces). We show that this approach provides a re-derivation of the Z-minimization criterion for AdS vacua giving the gravitational dual of a-maximization in 4d mathcal{N} = 1 toric quiver SCFTs.

Axion monodromy inflation, trapping mechanisms and the swampland

We study the effects of particle production on the evolution of the inflaton field in an axion monodromy model with the goal of discovering in which situations the resulting dynamics will be consistent with the swampland constraints. In the presence of a modulated potential the evolving background field (solution of the inflaton homogeneous in space) induces the production of long wavelength inflaton fluctuation modes. However, this either has a negligible effect on the inflaton dynamics (if the field spacing between local minima of the modulated potential is large), or else it traps the inflaton in a local minimum and leads to a graceful exit problem. On the other hand, the production of moduli fields at enhanced symmetry points can lead to a realization of trapped inflation consistent with the swampland constraints, as long as the coupling between the inflaton and the moduli fields is sufficiently large.

The adaptability of rice varieties on tidal swampland in South Kalimantan

Swampland was marginal land with considerable potential for rice farming. The key solution to overcome swampland constraints is nutrient, water, and plant management as well as the use of adaptive rice varieties. Inpara (Inbred swamp rice) is a variety released for adaptation to swampland. This research aimed to evaluate the adaptability of Inpara varieties in tidal swampland. The research was conducted at potential acid sulphate soil (Karang Bunga village, Barito Kuala regency) and actual acid sulphate soil (Barambai Kolam Kanan village, Barito Kuala regency). Randomized block design with three replications was applied to examine rice varieties. Data were collected and analyzed by variance analysis, if it is significant it will be tested with DMRT test. The result showed that there was a variation yield and adaptation (Fe score) among varieties tested. Some of the superior adaptive rice varieties were Inpara 1, Inpara 3, Inpara 4, Inpara 6, and Inpara 9 in tidal swampland. The average yield in potential acid sulphate soil was 37.9% higher than that of actual acid sulphate soil. The implication of this research was the variety of Inpara 1, Inpara 3, Inpara 4, Inpara 6, and Inpara 9 can be used as substitute varieties in the tidal swampland.

Swampland constraints on no-boundary quantum cosmology

The Hartle-Hawking no-boundary proposal describes the quantum creation of the universe. To have a non-negligible probability to obtain a classical expanding universe, eternal inflation is required, which is severely constrained by Swampland conjectures such as the refined de Sitter conjecture and the distance conjecture. We discuss this issue in detail and demonstrate the incompatibility. We show that the dimensionless parameters in the refined de Sitter conjecture should be bounded from above by a positive power of the scalar potential to realize the classical expanding universe. In other words, the probability of the classical expanding universe is extremely small under the Swampland conjectures unless the parameters are much smaller than unity. If they are order unity, on the other hand, the saddle-point solution itself ceases to exist implying a genuinely quantum universe.

Swampland, trans-Planckian censorship and fine-tuning problem for inflation: tunnelling wavefunction to the rescue

The trans-Planckian censorship conjecture implies that single-field models of inflation require an extreme fine-tuning of the initial conditions due to the very low-scale of inflation. In this work, we show how a quantum cosmological proposal—namely the tunneling wavefunction—naturally provides the necessary initial conditions without requiring such fine-tunings. More generally, we show how the tunneling wavefunction can provide suitable initial conditions for hilltop inflation models, the latter being typically preferred by the swampland constraints.

Non-canonical kinetic structures in the swampland

We consider how the swampland criteria might be applied to models in which scalar fields have nontrivial kinetic terms, particularly in the context of P(ϕ,X) theories, popularly used in approaches to inflation, to its alternatives, and to the problem of late-time cosmic acceleration. By embedding such theories in canonical multi-field models, from which the original theory emerges as a low-energy effective field theory, we derive swampland constraints, and study the circumstances under which these might be evaded while preserving cosmologically interesting phenomenology. We further demonstrate how these successes are tied to the phenomenon of turning in field space in the multi-field picture. We study both the general problem and specific examples of particular interest, such as DBI inflation.

Eternal inflation, entropy bounds and the swampland

It has been suggested that low energy effective field theories should satisfy given conditions in order to be successfully embedded into string theory. In the case of a single canonically normalized scalar field this translates into conditions on its potential and the derivatives thereof. In this Letter we revisit small field hilltop models of eternal inflation including stochastic effects and study the compatibility of the swampland constraints with entropy considerations. We show that these stochastic inflation scenarios either violate entropy bounds or the swampland criterion on the slope of the scalar field potential. Furthermore, we illustrate that such models are faced with a graceful exit problem: any patch of space which exits the region of eternal inflation is either not large enough to explain the isotropy of the cosmic microwave background, or has a spectrum of fluctuations with an unacceptably large red tilt.

Fermions and the Swampland

In this note we consider whether there could be Swampland constraints associated to the presence of fermions in the theory. We propose that any fermion must couple to an infinite tower of states, and that the mass scale of this tower, in Planck units, is set by the strength of the Yukawa coupling to the tower. This is a type of fermionic version of the (magnetic) Weak Gravity Conjecture. We also find that supersymmetry plays a natural part in this fermionic realisation, which motivates a further proposal that supersymmetry can only be broken below the scale set by this Yukawa coupling. We perform some preliminary checks in string theory of these ideas.

Swampland constraints on 5d mathcal{N} = 1 supergravity

We propose Swampland constraints on consistent 5-dimensional mathcal{N} = 1 supergravity theories. We focus on a special class of BPS magnetic monopole strings which arise in gravitational theories. The central charges and the levels of current algebras of 2d CFTs on these strings can be calculated by anomaly inflow mechanism and used to provide constraints on the low-energy particle spectrum and the effective action of the 5d supergravity based on unitarity of the worldsheet CFT. In M-theory, where these theories are realized by compactification on Calabi-Yau 3-folds, the special monopole strings arise from wrapped M5-branes on special (“semi-ample”) 4-cycles in the threefold. We identify various necessary geometric conditions for such cycles to lead to requisite BPS strings and translate these into constraints on the low-energy theories of gravity. These and other geometric conditions, some of which can be related to unitarity constraints on the monopole worldsheet, are additional candidates for Swampland constraints on 5-dimensional mathcal{N} = 1 supergravity theories.

Moduli Stabilisation and the Holographic Swampland

We investigate whether Swampland constraints on the low-energy dynamics of weakly coupled, moduli-stabilised string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. We find that various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to well-established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. The studied scenarios include LVS, KKLT, and both perturbative and racetrack stabilisation. Interestingly, the LVS vacuum (with $\Delta_{\varphi} = 8.038$) also appears to live very close to a critical value ($\Delta_{\varphi} = 8$) where the anomalous dimensions change sign. We finally point out an intriguing connection to the Swampland Distance Conjecture, both in its original and refined versions.

Scaling attractors in multi-field inflation

Multi-field inflation with a curved scalar geometry has been found to support background trajectories that violate the slow-roll, slow-turn conditions and thus have the potential to evade the swampland constraints. In order to understand how generic this novel behaviour is and what conditions lead to it, we perform a classification of dynamical attractors of two-field inflation that are of the scaling type. Scaling solutions form a one-parameter generalization of De Sitter solutions with a constant value of the first Hubble flow parameter ϵ and, as we argue and demonstrate, form a natural starting point for the study of non-slow-roll slow-turn behaviour. All scaling solutions can be classified as critical points of a specific dynamical system. We recover known multi-field inflationary attractors as approximate scaling solutions and classify their stability using dynamical system techniques. In particular, we discover that dynamical bifurcations play an integral role in the transition between geodesic and non-geodesic motion and discuss the ability of scaling solutions to describe realistic multi-field models. We revisit the criteria for background stability and show cases where the usual criteria found in the literature do not capture the background evolution of the system.

Modular symmetries and the swampland conjectures

Recent string theory tests of swampland ideas like the distance or the dS conjectures have been performed at weak coupling. Testing these ideas beyond the weak coupling regime remains challenging. We propose to exploit the modular symmetries of the moduli effective action to check swampland constraints beyond perturbation theory. As an example we study the case of heterotic 4d mathcal{N}=1 compactifications, whose non-perturbative effective action is known to be invariant under modular symmetries acting on the Kähler and complex structure moduli, in particular SL(2, Z) T-dualities (or subgroups thereof) for 4d heterotic or orbifold compactifications. Remarkably, in models with non-perturbative superpotentials, the corresponding duality invariant potentials diverge at points at infinite distance in moduli space. The divergence relates to towers of states becoming light, in agreement with the distance conjecture. We discuss specific examples of this behavior based on gaugino condensation in heterotic orbifolds. We show that these examples are dual to compactifications of type I’ or Horava-Witten theory, in which the SL(2, Z) acts on the complex structure of an underlying 2-torus, and the tower of light states correspond to D0-branes or M-theory KK modes. The non-perturbative examples explored point to potentials not leading to weak coupling at infinite distance, but rather diverging in the asymptotic corners of moduli space, dynamically forbidding the access to points with global symmetries. We perform a study of general modular invariant potentials and find that there are dS maxima and saddle points but no dS minima, and that all examples explored obey the refined dS conjecture.

Warm inflation as a way out of the swampland

We discuss how dissipative effects and the presence of a thermal radiation bath, which are inherent characteristics of the warm inflation dynamics, can evade the recently proposed Swampland conjectures. Different forms of dissipation terms, motivated by both microphysical quantum field theory and phenomenological models, are discussed and their viability to overcome the assumed Swampland constraints is analyzed.

Putting the boot into the swampland

The swampland program of delineating the space of effective field theories consistent with quantum gravity appears similar to the bootstrap program of delineating the space of quantum field theories consistent with conformal symmetry. With this in mind we rewrite the effective field theory of the Large Volume Scenario in AdS space solely in terms of RAdS, in a form suitable for holographic analysis. This rewritten EFT takes a remarkably universal (and previously unnoticed) form, which is uniquely determined in the large-volume limit up to terms suppressed by mathcal{O} (1/lnRAdS), with no reference to any of the fluxes, brane or instanton configurations that enter the microphysics of moduli stabilisation. The putative dual 3d CFT will have two low-lying single trace scalars, an even-parity scalar Φ dual to the volume modulus with {Delta}_{varPhi }=frac{3}{2}left(1+sqrt{19}right)simeq 8.038 and an odd-parity scalar a dual to the volume axion with Δa = 3. On the AdS side the higher-point interactions are likewise uniquely determined. As the AdS theory is both subject to swampland constraints and holographically related to a CFT, we argue that holography will lead to a ‘bootland’ — a map between swampland constraints on the AdS side and bootstrap constraints on the CFT side. We motivate this with a discussion of swampland quantum gravity constraints on the axion decay constant in the ν → ∞ limit and the 〈ΦΦaa〉 4-point function on the CFT side.

Runaway quintessence, out of the swampland

We propose a simple, well-motivated and robust alternative to a metastable de Sitter vacuum in string theory, consistent with current observations of dark energy and naturally satisfying conjectured swampland constraints. Inflation ends in a supersymmetric Minkowski minimum, with a flat direction that is protected by non-renormalisation theorems. At some scale non-perturbative effects kick in, inducing a runaway scalar potential. The tail of this runaway potential cannot sustain a late-time dominating, slow-roll quintessence. However, the potential always contains a dS maximum. If the modulus starts close to the hilltop, it remains frozen there by Hubble friction for much of the cosmological history, at first sourcing a tiny classical vacuum energy and then constituting a rolling quintessence, with observable consequences. So long as the modulus is localised away from the Standard Model in the extra dimensions, there are no observable fifth forces nor is there time-variation of fundamental constants, and the modulus mass is protected from radiative corrections. We revisit concrete string models based on heterotic orbifold compactifications, and show that their de Sitter extrema satisfy the recently refined dS Swampland Conjecture.