In the context of $\mathcal{N}=2$ supergravity without vector multiplets coupled to hypermultiplets, the coupling constant of graviphoton $τ$ is apriori a free parameter. Stringy realization of this and using a mathematical conjecture leads to the statement that $j(τ)\in \mathbb{R}$ so that the $θ$-angle is $0$ or $π$. We conjecture that for any consistent realization of $\mathcal{N}=2$ supergravity theories coupled only to hypermultiplets this is the case and the rest belong to the swampland. This leads to the speculation that the $θ$-angle for QCD or QED may also be fixed to $0$ for quantum gravitational consistency.
The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. Different proposals have been formulated in the form of Swampland conjectures. In these lecture notes, we provide a pedagogical introduction to the most important Swampland conjectures, their connections and their realization in string theory compactifications. The notes are based on the series of lectures given by Irene Valenzuela at the online QFT and Geometry summer school in July 2020.
We initiate the program of bottom-up derivation of string theory dualities using Swampland principles. In particular, we clarify the relation between Swampland arguments and all the string theory dualities in $d\geq9$ dimensional supersymmetric theories. Our arguments center around the sharpened distance conjecture and rely on various other Swampland principles.
We give a brief overview of the string landscape and techniques used to construct string compactifications. We then explain how this motivates the notion of the swampland and review a number of conjectures that attempt to characterize theories in the swampland. We also compare holography in the context of superstrings with the similar, but much simpler case of topological string theory. For topological strings, there is a direct definition of topological gravity based on a sum over a "quantum gravitational foam." In this context, holography is the statement of an identification between a gravi…
We study the weak gravity conjecture, the swampland distance conjecture and the emergence proposal for $\mathcal{N}=1$ orientifold compactifications of type IIB string theory with O3-/O7-planes. We allow for orientifold projections with $h^{2,1}_+\neq 0$ which gives rise to closed-string $U(1)$ gauge fields, and our findings show that certain structures present for $\mathcal N=2$ compactifications are not present for $\mathcal N=1$. In particular, assumptions about stability have to be relaxed and we encounter an ambiguity for the emergence of gauge symmetries associated with the $h^{2,1}_+$ s…
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 $\frac12$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 coupli…
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.
Recent developments in string theory suggest that string theory landscape of vacua is vast. It is natural to ask if this landscape is as vast as allowed by consistent-looking effective field theories. We use universality ideas from string theory to suggest that this is not the case, and that the landscape is surrounded by an even more vast swampland of consistent-looking semiclassical effective field theories, which are actually inconsistent. Identification of the boundary of the landscape is a central question which is at the heart of the meaning of universality properties of consistent quant…
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 this essay we will take a wonderful ride on a dark bubble with strings attached, which carries our universe out of the swampland and makes it realizable in the landscape of string theory. To find the way to the landscape, we make use of apparently hostile corners of the swampland and their instabilities.
We make a number of conjectures about the geometry of continuous moduli parameterizing the string landscape. In particular we conjecture that such moduli are always given by expectation value of scalar fields and that moduli spaces with finite non-zero diameter belong to the swampland. We also conjecture that points at infinity in a moduli space correspond to points where an infinite tower of massless states appear, and that near these regions the moduli space is negatively curved. We also propose that there is no non-trivial 1-cycle of minimum length in the moduli space. This leads in particu…
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.
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 …
The refined swampland de Sitter conjecture (SdSC) is a proposed constraint on the form of the total potential in a theory including quantum gravity. According to this conjecture potentials possessing metastable de Sitter vacua are in the swampland of effective field theories that cannot descend from a theory with gravity. It is known that in the Standard Model (SM), as the quark masses and theta-parameter are varied, IR- calculable metastable states in QCD appear (for N > 2 light quarks) and we discuss in detail their properties. We argue that the SdSC excludes the values of quark masses and t…
We consider supergravity theories with 16 supercharges in Minkowski space with dimensions $d>3$. We argue that there is an upper bound on the number of massless modes in such theories depending on $d$. In particular we show that the rank of the gauge symmetry group $G$ in $d$ dimensions is bounded by $r_G\leq 26-d$. This in particular demonstrates that 4 dimensional ${\cal N}=4$ SYM theories with rank bigger than 22, despite being consistent and indeed finite before coupling to gravity, cannot be consistently coupled to ${\cal N}=4$ supergravity in Minkowski space and belong to the swampland. …
Recently, Kim, Shiu and Vafa proposed general consistency conditions for six dimensional supergravity theories with minimal supersymmetry coming from couplings to strings. We test them in explicit perturbative orientifold models in order to unravel the microscopic origin of these constraints. Based on the perturbative data, we conjecture the existence of null charges $Q \cdot Q=0 $ for any six-dimensional theory with at least one tensor multiplet, coupling to string defects of charge $Q$. We then include the new constraint to exclude some six-dimensional supersymmetric anomaly-free examples th…
The landscape of possible four-dimensional low-energy effective theories arising from compactifications of string/M-theory seems vast. This might lead one to believe that any consistent-looking effective field theory coupled to gravity can be obtained as a low-energy limit of string theory. However, a set of "swampland" conjectures suggests that this is not true and that, in fact, there is an even larger set of effective field theories that cannot be obtained in this way. In particular, the AdS instability swampland conjecture asserts that nonsupersymmetric anti-de Sitter vacua are unstable. T…
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 String Gas Cosmology, the simplest shape modulus fields are naturally stabilized by taking into account the presence of string winding and momentum modes. We determine the resulting effective potential for these fields and show that it obeys the de Sitter conjecture, one of the swampland criteria for effective field theories to be consistent with superstring theory.
We argue that under certain assumptions the quantum break time approach and the trans-Planckian censorship conjecture both lead to de Sitter swampland constraints of the same functional form. It is a well known fact that the quantum energy-momentum tensor in the Bunch-Davies vacuum computed in the static patch of dS breaks some of the isometries. Proposing that this is a manifestation of quantum breaking of dS, we analyze some of its consequences. In particular, this leads to a thermal matter component that can be generalized to string theory in an obvious way. Imposing a censorship of quantum…
The transcendental expectation of string theory is that the nature of the fundamental forces, particle spectra and masses, together with coupling constants, is uniquely determined by mathematical and logical consistency, non-empirically, that is by pure reason. However pluralism triumphed with the explosive emergence of the multiverse. String theorists have extended a long-sought dream (their unique and final theory) to a landscape or a happy caparnaum. Proponents of string theory try to qualify their arguments via swampland conjectures while cosmologists retreat to their telescopes. We review…
The "swampland conjectures" have been recently suggested as a set of criteria to assess if effective field theories (EFTs) are consistent with a quantum gravity embedding. Such criteria, which restrict the behavior of scalar fields in the theory, have strong implications for cosmology in the early universe. As we demonstrate, they will also have direct consequences for formation of primordial black holes (PBHs) and dark matter (DM).
We continue the investigation of F-term axion monodromy inflation in string theory, while seriously taking the issue of moduli stabilization into account. For a number of closed and open string models, we show that they suffer from serious control issues once one is trying to realize trans-Planckian field excursions. More precisely, the flux tuning required to delay the logarithmic scaling of the field distance to a trans-Planckian value cannot be done without leaving the regime where the employed effective supergravity theory is under control. Our findings are consistent with the axionic exte…
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…
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 sharpen Swampland constraints on 8d supergravity theories by studying consistency conditions on worldvolume theory of 3-brane probes. Combined with a stronger form of the cobordism conjecture, this leads to the reconstruction of the compact internal geometry and implies strong restrictions on the gauge algebra and on some higher derivative terms (related to the level of the current algebra on the 1-brane). In particular we argue that 8d supergravity theories with $\mathfrak{g}_2$ gauge symmetry are in the Swampland. These results provide further evidence for the string lamppost principle in…
In this paper, we study some aspects of moduli stabilization using string gases in the context of the Swampland. In the framework which we derive, the matter Lagrangian for string gases yields a potential for the size moduli which satisfies the de Sitter conjecture with the condition $\frac{|\nabla V|}{V} \geq \frac{1}{\sqrt{p}}\frac{1}{M_p}$, where $p$ is the number of compactified dimensions. Moreover, the moduli find themselves stabilized at the self-dual radius, and gravity naturally emerges as the weakest force.
Attempts to construct string derived effective field theory models realizing large field inflation are plagued by control issues. Targeted at a broader audience, in this article we review recent progress in isolating the underlying conceptual reasons for this failure. Special emphasis is given to models of axion monodromy inflation and their relation to the Swampland Distance Conjecture. This discriminates effective actions that admit a UV completion, the landscape, from those that do not, the swampland. Since they are conceptually very similar, we also comment on implied challenges for axioni…
Global Asymptotics, the Swampland Conjectures, and Preheating of String Moduli
Center for Theoretical Physics—a Leinweber Institute, Department of Physics, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Department of Physics and Astronomy, University of Oklahoma（俄克拉荷马大学物理与天文学系）；Department of Physics, University of Wisconsin, Madison（威斯康星大学麦迪逊分校物理系）
We analyze AdS and dS swampland conjectures in a three-dimensional higher spin theory with self-interacting matter, which contains conformal gravity and is almost topological. A theory of a similar type was proposed as the effective theory in the high energy phase of non-critical M-theory in 3D. With some details differing from the usual string theory story, it is found that the resulting effective theory, namely topologically massive gravity, fits well into the web of the proposed swampland conjectures. Supporting a recent proposal, in particular we find that this 3D theory gives rise to a qu…
We propose Swampland constraints on consistent 5-dimensional ${\cal N}=1$ 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 strin…
We consider single-field inflation in light of string-motivated "swampland" conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion $Δϕ\lesssim M_{\rm Pl}$, in combination with a sufficiently steep potential, $M_{\rm Pl} V_ϕ/V \gtrsim {\cal O}(1)$. Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the $n_S$-$r$ "zoo plot" of inflationary models, …
One class of single-field inflationary models compatible with the recently-conjectured Swampland criteria would be those in which a Hubble slow-roll parameter $ε_\text{H}$ is not the same as $ε_\text{V} \sim (V'/V)^2$. However, a roadblock for these models (with a convex potential) lie in the unacceptably high tensor-to-scalar ratio, $r$, generically predicted by them. In this work, illustrating through an explicit example, we point out that having a non-Bunch-Davies component to the initial state of cosmological perturbations makes the value of $r$ compatible with observations. In this way, w…
The Swampland Distance Conjecture claims that effective theories derived from a consistent theory of quantum gravity only have a finite range of validity. This will imply drastic consequences for string theory model building. The refined version of this conjecture says that this range is of the order of the naturally built in scale, namely the Planck scale. It is investigated whether the Refined Swampland Distance Conjecture is consistent with proper field distances arising in the well understood moduli spaces of Calabi-Yau compactification. Investigating in particular the non-geometric phases…
In this Letter, we study the implications of string Swampland criteria for dark energy in view of ongoing and future cosmological observations. If string theory should be the ultimate quantum gravity theory, there is evidence that exact de Sitter solutions with a positive cosmological constant cannot describe the fate of the late-time universe. Even though cosmological models with dark energy given by a scalar field $π$ evolving in time are not in direct tension with string theory, they have to satisfy the Swampland criteria $|Δπ|<d\sim\mathcal{O}(1)$ and $|V'|/V>c\sim\mathcal{O}(1)$, where $V…
We study constraints imposed by two proposed string Swampland criteria on cosmology. These criteria involve an upper bound on the range traversed by scalar fields as well as a lower bound on $|\nabla_ϕ V|/V$ when $V >0$. We find that inflationary models are generically in tension with these two criteria. Applying these same criteria to dark energy in the present epoch, we find that specific quintessence models can satisfy these bounds and, at the same time, satisfy current observational constraints. Assuming the two Swampland criteria are valid, we argue that the universe will undergo a phase …
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…
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.
EFTs with Symmetric Moduli Spaces: the Landscape and the Swampland
Abdus Salam Centre for Theoretical Physics, Imperial College London（帝国理工学院阿卜杜斯·萨拉姆理论物理中心）；Instituto de Física Teórica UAM/CSIC（马德里自治大学/西班牙国家研究委员会理论物理研究所）；Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS（巴黎萨克雷大学CEA-CNRS理论物理研究所）；Max-Planck-Institut für Physik（马克斯·普朗克物理学研究所）
It was recently pointed out that the existence of dark energy imposes highly restrictive constraints on effective field theories that satisfy the Swampland conjectures. We provide a critical confrontation of these constraints with the cosmological framework emerging from the Salam-Sezgin model and its string realization by Cvetic, Gibbons, and Pope. We also discuss the implication of the constraints for string model building.
Completeness of the spectrum of charged branes in a quantum theory of gravity naturally motivates the question of whether consistency of what lives on the branes can be used to explain some of the Swampland conditions. In this paper we focus on consistency of what lives on string probes, to show some of the theories with ${\cal N}=(1,0)$ supersymmetry in 10d and 6d, which are otherwise consistent looking, belong to the Swampland. Gravitational and gauge group anomaly inflow on these probes can be used to compute the gravitational central charges $(c_L,c_R)$ as well as the level of the group's …
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…
The First and Second Swampland Conjectures (FSC & SSC) are substantially modified in non-critical string cosmology, in which cosmic time is identified with the time-like Liouville mode of the supercritical string. In this scenario the Friedmann equation receives additional contributions due to the non-criticality of the string. These are potentially important when one seeks to apply the Bousso bound for the entropy of states that may become light as the dilaton takes on trans-Planckian values, as in a de Sitter phase, and restore consistency with the FSC and in at least some cases also the SSC…
We consider quintessence models within 4D effective descriptions of gravity coupled to two scalar fields. These theories are known to give rise to viable models of late-time cosmic acceleration without any need for flat potentials, and so they are potentially in agreement with the dS Swampland conjecture. In this paper we investigate the possibility of consistently embedding such constructions in string theory. We identify situations where the quintessence fields are either closed string universal moduli or non-universal moduli such as blow-up modes. We generically show that no trajectories co…
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…
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…
Swampland conjecture has been recently proposed to connect early time cosmological models with the string landscape, and then to understand if related scalar fields and potentials can come from some fundamental theory in the high energy regime. In this paper, we discuss swampland criteria for $f(R)$ gravity considering models where duality symmetry is present. In this perspective, specific $f(R)$ models can naturally belong to the string landscape. In particular, it is possible to show that duality is a Noether symmetry emerging from dynamics. The selected $f(R)$ models, satisfying the swampla…
In this work we examine the Swampland criteria for a specific class of rescaled $f(R)$ gravitational models, that are capable of unifying the primordial era of the Universe with the late-time era with the inclusion of string corrections. In particular, we develop separately the theoretical framework of Gauss-Bonnet and Chern-Simons theories considering that, the rescale parameter is constrained to reside in the area $0<α<1$. As showcased, in the context of the aforementioned theories, a viable inflationary phenomenology consistent with the latest Planck data can be obtained for both cases for …
