The Swampland program relies heavily on the conjecture that there can only be a finite number of flux vacua (FFV conjecture). Stipulating this FFV conjecture and applying it to some older work in flux vacua construction we show that within a patch of the landscape the FFV conjecture makes predictions on the non-existence of otherwise viable non-perturbative objects arising from brane recombination. Future gains in direct non-perturbative analysis could therefore not only test this prediction but also test portions of the Swampland program itself. We also discuss implications of a weaker FFV conjecture on the counting of flux vacua which predicts positivity of the brane central charge if the EFT analysis is to be qualitatively trusted.
It was recently argued that the swampland distance conjecture rules out dS vacua at parametrically large field distances. We point out that this conclusion can in principle be avoided in the presence of large fluxes that are not bounded by a tadpole cancellation condition. We then study this possibility in the concrete setting of classical type IIA flux compactifications with (anti-)O6-planes, (anti-)D6-branes and/or KK monopoles and show that, nonetheless, parametrically controlled dS vacua are strongly constrained. In particular, we find that such dS vacua are ruled out at parametrically lar…
We discuss the properties of massive type IIA flux compactifications. In particular, we investigate in which case one can obtain dS vacua at large volume and small coupling. We support a general discussion of scaling symmetries with the analysis of a concrete example. We find that the large volume and weak coupling limit requires a large number of O6-planes. Since these are bound for any given compactification space one cannot get arbitrarily good control over $α'$ and string loop corrections.
It has recently been conjectured that string theory does not admit de Sitter critical points. This note points out that in several cases, including KKLT or racetrack models, this statement is equivalent to the absence of supersymmetric Minkowski or AdS solutions. This equivalence arises from establishing the positivity of the potential in a large-radius limit, requiring a turnover of the potential before reaching an AdS vacuum. For example, this conjecture is incompatible with the simplest 1-modulus KKLT AdS supersymmetric solution.
In recent times, a considerable effort has been dedicated to identify certain conditions -- the so-called swampland conjectures -- with an eye on identifying effective theories which have no consistent UV-completions in string theory. In this paper, we examine the anti-de Sitter vacua corresponding to solutions which arise from purely non-perturbative contributions to the superpotential and show that these solutions satisfy the (axionic) weak gravity conjecture and the AdS-moduli scale separation conjecture. We also sketch out their advantages over other constructions.
In this paper we propose a quantum version of the swampland conjecture. We argue that quantum instabilities of de Sitter space discovered using field theoretical methods, are directly related to the difficulties in finding stringy de Sitter vacua.
We extend studies of holographic aspects of moduli stabilisation scenarios to both fibred versions of LVS and the type IIA DGKT flux vacua. We study the holographic properties of the low-energy moduli Lagrangian that describes both the AdS vacuum and also small perturbations about it. For type IIA vacua in the large-volume regime, the CFT data (operator dimensions and higher-point interactions) take a universal form independent of the many arbitrary flux choices, as was previously found for LVS stabilisation. For these IIA vacua the conformal dimensions of the dual operators are also, surprisi…
It has been notoriously difficult to construct a meta-stable de Sitter (dS) vacuum in string theory in a controlled approximation. This suggests the possibility that meta-stable dS belongs to the swampland. In this paper, we propose a swampland criterion in the form of $|\nabla V|\geq\ c \cdot V$ for a scalar potential $V$ of any consistent theory of quantum gravity, for a positive constant $c$. In particular, this bound forbids dS vacua. The existence of this bound is motivated by the abundance of string theory constructions and no-go theorems which exhibit this behavior. We also extend some …
We view and provide further evidence for a number of Swampland criteria, including the Weak Gravity Conjecture, Distance Conjecture and bounds on the finiteness of the quantum gravity vacua from the prism of the finiteness of black hole entropy. Furthermore we propose that at least all of these Swampland statements may be more fundamentally a consequence of the finiteness of quantum gravity amplitudes.
We point out that the de Sitter swampland conjecture would be falsified if classical fluxed Type IIA orientifold vacua with a single non-BPS D7-brane were indeed part of the string theory landscape. In other words, the dS swampland conjecture implies the cancellation of K-theory charges on a compact space.
In this note we revisit some of the recent 10d and 4d arguments suggesting that uplifting of supersymmetric AdS vacua leads to flattening of the potential, preventing formation of dS vacua. We explain why the corresponding 10d approach is inconclusive and requires considerable modifications. We also show that while the flattening effects may occur for some extreme values of the parameters, they do not prevent the formation of dS vacua within the range of validity of the 4d KKLT models. The KL version of the KKLT scenario based on a racetrack superpotential requires parametrically small uplifti…
We review some aspects of the dramatic consequences of supersymmetry breaking on string vacua. In particular, we focus on the issue of vacuum stability in ten-dimensional string models with broken, or without, supersymmetry, whose perturbative spectra are free of tachyons. After formulating the models at stake, we introduce their unified low-energy effective description and present a number of vacuum solutions to the classical equations of motion. In addition, we present a generalization of previous no-go results for de Sitter vacua in warped flux compactifications. Then we analyze the classic…
We investigate the vacuum structure of four-dimensional effective theory arising from Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold, corresponding to a T-dual of the DeWolfe-Giryavets-Kachru-Taylor model in Type IIA flux compactifications. By analyzing the vacuum structure of this interesting corner of string landscape, it turns out that there exist perturbatively unstable de Sitter (dS) vacua in addition to supersymmetric and non-supersymmetric anti-de Sitter vacua. On the other hand, the stable dS vacua appearing in the low-energy effective action violate the …
We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial. In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes. On the other hand, the non-Abelian structure of the IIB duality group $SL(2,\mathbb{Z})$ implies the existence of additional $[p,q]$ 7-branes. We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton. This description allows to recover t…
Recently it has been conjectured that string theory does not allow for dS vacua or dS extrema. To scrutinize such a conjecture, it is important to study concrete string theory compactifications and spell out their assumptions and potential shortcomings. We do so for one particular class of string compactifications, namely classical compactifications of type II string theory with fluxes, D-branes and O-planes on manifolds with SU(3) structure. In particular, we revisit previously found dS critical points, construct many new ones and check whether they invalidate the dS swampland conjecture.
We observe that racetrack models for moduli stabilization are in tension with strong forms of the Weak Gravity Conjecture (WGC). Moreover, recently, it was noted that controlled KKLT-type de Sitter vacua seem to require a racetrack fine-tuning of the type introduced by Kallosh and Linde. We combine these observations and conclude that the quests for realizing parametrically large axion decay constants and controlled de Sitter vacua are intimately related. Finally, we discuss possible approaches to curing the conflict between the racetrack scheme and the WGC.
Compactifying the Standard Model (SM) on a circle may lead to AdS 3D vacua, depending on the character (Majorana or Dirac) and the mass of the lightest neutrino. It has been shown that, imposing the Ooguri-Vafa conjecture that no stable non-SUSY AdS vacua are consistent with Quantum Gravity, one can obtain conditions on the mass of the lightest neutrino. This result has the shortcoming that it is in general sensitive to the UV structure of the theory. In the present paper we show that two other independent swampland conditions may yield constraints very similar to those. These other two condit…
We present a conjecture for the massless sector of perturbative 4D $N=1$ heterotic $(0,2)$ string vacua, including $U(1)^n$ gauge symmetries,one of them possibly anomalous (like in standard heterotic compactifications). Mathematically it states that the positive hull generated by the charges of the massless chiral multiplets spans a sublattice of the full charge lattice. We have tested this conjecture in many heterotic $N=1$ compactifications in 4D. Our motivation for this conjecture is that it allows to understand a very old puzzle in $(0,2)$ $N=1$ heterotic compactification with an anomalous…
We consider Type IIB compactifications on an isotropic torus $T^6$ threaded by geometric and non geometric fluxes. For this particular setup we apply supervised machine learning techniques, namely an artificial neural network coupled to a genetic algorithm, in order to obtain more than sixty thousand flux configurations yielding to a scalar potential with at least one critical point. We observe that both stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the Refined de Sitter Con…
Recently, various swampland conjectures have been proposed that every UV complete effective field theory should satisfy. In particular, these deal with the properties of AdS and dS solutions arising in theories of quantum gravity. Mainly summarizing the results of our two previous articles arXiv:1902.07724 and arXiv:1910.10185, we confront the string theory based KKLT scenario with these conjectures and argue that if quantum vacua as in the KKLT construction indeed exist, some of the conjectures receive some log-corrections. Furthermore we point out some new aspects not contained in the aforem…
We compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3)$\,\times\,$SO(3)-invariant AdS$_4$ vacuum of 11-dimensional supergravity, whose lowest-lying Kaluza-Klein modes belong to a consistent truncation to 4-dimensional ${\cal N}=8$ supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS$_4$ vacuum is perturbatively unstable within 11-dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes and provides further evidence for the AdS swampland conjecture, which …
We study supersymmetric AdS$_7$ vacua of massive type IIA string theory, which were argued to describe the near-horizon limit of NS5/D6/D8-brane intersections and to be holographically dual to 6D $(1,0)$ theories. We show, for the case without D8-brane charges, that such vacua do not admit any supersymmetry-breaking deformations. Our result implies that the dual $(1,0)$ theories do not have a conformal manifold, thus extending previously known results for supersymmetric deformations. It is also in line with the recent conjecture that non-supersymmetric AdS vacua are in the swampland.
The scalar potential of recombination fields of magnetized branes in Type IIB orientifold compactifications is analyzed in the absence of any closed string fluxes. Considering its perturbative F and D-term contributions in a quadratic approximation, we present the conditions for which its minima are supersymmetric. We show that for reasonable conditions on the spectrum, both metric moduli and recombination fields can be stabilized. We then provide explicit examples of compact manifolds where a Minkowski vacuum is realized in a Higgs phase. The vacuum energy is zero and some charged scalars acq…
Based on the flux-scaling scenario we study a model consisting on Type IIB string theory compactified on a Calabi-Yau manifold with a frozen complex structure in the presence of generic fluxes. The model contains (meta)stable Minkowski and de Sitter vacua as well as inflationary directions driven by two independent linear combination of axions. Due to a numerical control by fluxes, we show that cosmological parameters as the spectral index, tensor-to-scalar ratio and non-Gaussianities can be kept within observed bounds while preserving the desired hierarchies on physical scales. Moreover we co…
We elaborate on the recent work of Moritz et. al. where it is argued that anti-brane uplifting in KKLT models never leads to dS vacua. This is due to flattening effects in the effective potential found when treating the gaugino condensate energy momentum in ten-dimensional supergravity. We point out that the Silverstein-Saltman uplift, which effectively dissolves the anti-brane in 3-form fluxes, is a conceptually simpler setting in which flattening effects can be present, without requiring assumptions about UV/IR mixings. Along the way we revise and improve on the arguments of Moritz et. al. a…
Realising de Sitter vacua in string theory is challenging. For this reason it has been conjectured that de Sitter vacua inhabit the Swampland of inconsistent low-energy effective theories coupled to gravity. Since de Sitter is an attractor for $Λ$CDM, the conjecture calls $Λ$CDM into question. Reality appears sympathetic to this idea as local measurements of the Hubble constant $H_0$ are also at odds with $Λ$CDM analysis of Planck data. This tension suggests that the de Sitter state is unstable, thereby implying a turning point in the Hubble parameter. We present a model relieving this tension…
We provide an overview of the string landscape and the Swampland program. Our review of the string landscape covers the worldsheet and spacetime perspectives, including vacua and string dualities. We then review and motivate the Swampland program from the lessons learned from the string landscape. These lecture notes are aimed to be self-contained and thus can serve as a starting point for researchers interested in exploring these ideas. These notes are an expanded version of two courses "The String Landscape and the Swampland" taught by C.~Vafa at Harvard University in 2018 with a focus on th…
In a previous work, we noted that vacua with higher flux could be obtained by recombination of a small set of hidden-sector branes, numbering up to the Kahler degrees of freedom left to be fixed in the problem. Here, we discuss the general construction of Type IIB Standard Model flux vacua in which multiple branes participate in brane recombination in the hidden sector. We present several models with 4, 5 and 10 branes in a stack. They are complete with Pati-Salam gauge group, Standard Model chiral matter, and a hidden sector that combines with nonzero flux to satisfy RR tadpole constraints. W…
AdS flux vacua with a parametric separation between the AdS and KK scales have been conjectured to be in the Swampland. We study flux compactifications of massive IIA supergravity with O6 planes which are claimed to allow moduli-stabilised and scale separated AdS$_3$ and AdS$_4$ vacua at arbitrary weak coupling and large volume. A recent refinement of the AdS Distance Conjecture is shown to be inconsistent with the class of AdS$_3$ vacua because the requisite discrete higher form symmetries are absent. We further perform a tree-level study of non-perturbative decays for the nonsupersymmetric v…
Recently proposed de Sitter Swampland conjectures imply non-trivial constraints on a scalar field potential in any effective field theory that admits a quantum gravity completion. The original conjecture apparently excludes many phenomenologically motivated scalar potentials with de Sitter extrema, such as the perturbative Standard Model Higgs potential and the QCD axion potential, as the viable low-energy theories. Subsequently, the refined, weaker conjecture was proposed. However, the full effective potential, having been defined as a Legendre transform, is necessarily convex. This ensures t…
We study moduli stabilization for type IIB orientifold compactifications on Calabi-Yau three-folds with (non-)geometric fluxes. For this setting it is possible to stabilize all closed-string moduli classically without the need for non-perturbative contributions, and examples of stable de-Sitter constructions can be found in the literature which violate a prominent swampland conjecture. In this paper we derive general properties of non-geometric flux-compactifications, we argue that the contribution of fluxes to the tadpole cancellation conditions should be similar to D-branes (and not anti-D-b…
We initiate the systematic study of flux scalar potentials and their vacua by using asymptotic Hodge theory. To begin with, we consider F-theory compactifications on Calabi-Yau fourfolds with four-form flux. We argue that a classifications of all scalar potentials can be performed when focusing on regions in the field space in which one or several fields are large and close to a boundary. To exemplify the constraints on such asymptotic flux compactifications, we explicitly determine this classification for situations in which two complex structure moduli are taken to be large. Our classificati…
In this thesis we have studied various applications of asymptotic Hodge theory in string compactifications. This mathematical framework captures how physical couplings of the resulting effective theories behave near field space boundaries where the internal Calabi-Yau manifold degenerates. Below we summarize the three parts in which this thesis is divided. Part I introduces the techniques from asymptotic Hodge theory we used throughout this thesis. We review the results of the nilpotent orbit theorem of Schmid and the multi-variable sl(2)-orbit theorem of Cattani, Kaplan and Schmid. This discu…
We investigate the transmutation of D-branes into Abelian magnetic backgrounds on the world-volume of higher-dimensional branes, within the framework of global models with compact internal dimensions. The phenomenon, T-dual to brane recombination in the intersecting-brane picture, shares some similarities to inverse small-instanton transitions in non-compact spaces, though in this case the Abelian magnetic background is a consequence of the compactness of the internal manifold, and is not ascribed to a zero-size non-Abelian instanton growing to maximal size. We provide details of the transitio…
We point out that the swampland conjectures, forbidding the presence of global symmetries and (meta-)stable de Sitter vacua within quantum gravity, pick up a dynamical axion for the electroweak SU(2) gauge theory as a natural candidate for the quintessence field. The potential energy of the electroweak axion provides an attractive candidate for the dark energy. We discuss constraints from the weak gravity conjecture, from the conjecture of no global symmetry, and from observations, which can be satisfied elegantly in a supersymmetric extension of the standard model.
We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at a finite distance, in a dynamical realization of the Cobordism Conjecture. We show that as the configuration approaches these cobordism walls of nothing, the scalar fields run off to infinite distance in moduli space, allowing to explore the implications of the Swampland Distance Conjecture. We uncover new interesting scaling relations linking the moduli sp…
We revisit flux compactifications of type IIB string theory on `spaces' dual to rigid Calabi-Yau manifolds. This rather unexplored part of the string landscapes harbors many interesting four-dimensional solutions, namely supersymmetric $\mathcal{N}=1$ Minkowski vacua without flat direction and infinite families of AdS vacua, some potentially with unrestricted rank for the gauge group. We also comment on the existence of metastable dS solutions in this setup. We discuss how these solutions fit into the web of swampland conjectures.
The Swampland Distance Conjecture states that at infinite distance in the scalar moduli space an infinite tower of particles become exponentially massless. We study this issue in the context of 4d type IIA and type IIB Calabi-Yau compactifications. We find that for large moduli not only towers of particles but also domain walls and strings become tensionless. We study in detail the case of type IIA and IIB ${\cal N}=1$ CY orientifolds and show how for infinite Kähler and/or complex structure moduli towers of domain walls and strings become tensionless, depending on the particular direction in …
We construct AdS$_4$ flux vacua of type IIA string theory in the supergravity (large volume, small $g_s$) regime, including the backreaction of O6-planes. Our solutions are the localized versions of the smeared solutions on Calabi-Yau orientifolds studied by DeWolfe, Giryavets, Kachru and Taylor and in other works. We find that the O-plane backreaction in these solutions generates warping, a varying dilaton, non-closed RR field strengths and internal curvature. Just like their smeared counterparts, the localized solutions admit stabilized moduli, a parametric control over string corrections an…
One of the main goals of the field of string phenomenology is to describe the properties of our spacetime in low-energy effective models related to and consistent with string theory. It is known that our universe undergoes accelerated expansion, which can be described in Einstein's theory of general relativity as a positive cosmological constant. Within string theory descriptions, this is realized by a scalar field with a positive value of its potential. Oftentimes, this is modeled by having the scalar at a stable, positive minimum. One then obtains a de Sitter spacetime. Constructions of de S…
Nongeometric flux compactifications with frozen complex structure moduli have been recently studied for several phenomenological purposes. In this context, we analyze the possibility of realizing de-Sitter solutions in the context of ${\cal N} =1$ type II nongeometric flux compactifications using the ${\mathbb T}^6/({\mathbb Z}_3 \times {\mathbb Z}_3)$ toroidal orientifolds. For the type IIB case, we observe that the Bianchi identities are too strong to simultaneously allow both the NS-NS three-form flux ($H_3$) and the nongeometric ($Q$) flux to take non-zero values, which makes this model ir…
Stable non-supersymmetric Anti-de Sitter (AdS) vacua of string theory are widely believed not to exist. In this letter, we analytically compute the full bosonic Kaluza-Klein spectrum around the ${\rm G_2}$-invariant non-supersymmetric $\textrm{AdS}_4$ solution of massive IIA supergravity, and show that it is perturbatively stable. We also provide evidence that six other non-supersymmetric $\textrm{AdS}_4$ solutions of massive IIA supergravity are perturbatively stable. Since previous studies have indicated that these AdS vacua may also be non-perturbatively stable, our findings pose a challeng…
Motivated by the recently proposed de Sitter swampland conjecture, a formally same condition imposed instead on the convex and real exact effective potential is contemplated. Compared to the original conjecture, the modified condition admits a broader class of low-energy effective theories such as those with local maxima and/or false de Sitter vacua with some restrictions, as long as there is an anti-de Sitter vacuum. The observed accelerating expansion of the universe might therefore be attributed to a quintessence or a metastable vacuum. The former solution can be simplified and thus better …
I conjecture an upper bound on the number of possible swampland conjectures by comparing the entropy required by the conjectures themselves to the Beckenstein-Hawking entropy of the cosmological horizon. Assuming of order 100 kilobits of entropy per conjecture, this places an upper bound of order $10^{117}$ on the number of conjectures. I estimate the rate of production of swampland conjectures by the number of papers listed on INSPIRE with the word "swampland" in the title or abstract, which has been showing approximately exponential growth since 2014. At the current rate of growth, the entro…
We consider the SU(2)LxSU(2)R Standard Model brane embedding in an orientifold of T6/Z2xZ2. Within defined limits, we construct all such Standard Model brane embeddings and determine the relative number of flux vacua for each construction. Supersymmetry preserving brane recombination in the hidden sector enables us to identify many solutions with high flux. We discuss in detail the phenomenology of one model which is likely to dominate the counting of vacua. While Kahler moduli stabilization remains to be fully understood, we define the criteria necessary for generic constructions to have fixe…
We study brane recombination for supersymmetric configurations of intersecting branes in terms of the world-volume field theory. This field theory contains an impurity, corresponding to the degrees of freedom localized at the intersection. The Higgs branch, on which the impurity fields condense, consists of vacua for which the intersection is deformed into a smooth calibrated manifold. We show this explicitly using a superspace formalism for which the calibration equations arise naturally from F- and D-flatness.
We provide a detailed discussion of the main theoretical and phenomenological challenges of quintessence model building in any numerically controlled regime of the moduli space of string theory. We argue that a working quintessence model requires a leading order non-supersymmetric (near) Minkowski vacuum with an axionic flat direction. This axion, when lifted by subdominant non-perturbative effects, could drive hilltop quintessence only for highly tuned initial conditions and a very low inflationary scale. Our analysis has two important implications. Firstly, scenarios which are in agreement w…
We generalize the swampland criterion forbidding stable non-supersymmetric AdS vacua and propose a new swampland conjecture forbidding stable non-supersymmetric "locally AdS" warped throats. The conjecture is motivated by the properties of systems of fractional D3-branes at singularities, and can be used to rule out large classes of warped throats with supersymmetry breaking ingredients, and their possible application to de Sitter uplift. In particular, this allows to reinterpret the runaway instabilities of the gravity dual of fractional branes in the dP$_1$ theory, and to rule out warped thr…
We consider constraints on $D$-dimensional theories in $M_D$, $dS_D$ and $AdS_D$ backgrounds in the light of AdS swampland conjectures as applied to their compactification in a circle. In particular we consider the non-SUSY AdS instability conjecture and the AdS distance conjecture. For $M_D$ and $dS_D$ vacua the results may be summarized by a light fermion conjecture which states that in theories with $Λ_D\geq 0$ and a positive first non-vanishing supertrace $(-1)^{k+1}\text{Str} M^{2k}>0$, a surplus of light fermions with mass $m_f\lesssim Λ_D^{1/D}$ must be present. On the contrary, the cas…
Recently a swampland criterion has been proposed that rules out de Sitter vacua in string theory. Such a criterion should hold at all points in the field space and especially at points where the system is on-shell. However there has not been any attempt to examine the swampland criterion against explicit equations of motion. In this paper we study four-dimensional de Sitter and quasi-de Sitter solutions using dimensionally reduced M-theory. While on one hand all classical sources that could allow for solutions with de Sitter isometries are ruled out, the quantum corrections, on the other hand,…
We discuss the process of transmutation of branes into Abelian magnetic flux on the worldvolume of $D9$ branes. This phenomenon is T-dual to the recombination of branes in the intersecting-brane description. In the low energy limit this can be described by a Higgs mechanism involving bifundamental scalars. The Abelian magnetic background arises as a consequence of the compactness of the internal space. Explicit (six-dimensional) examples based on the supersymmetric and the Brane Supersymmetry Breaking (BSB) \mathbb{T}^4/\mathbb{Z}_2 orientifold are analyzed.
