198 Pages, 40 figures. Invited review for Fortschritte der Physik. Partially based on lectures delivered at BUSSTEPP 2018 (Oxford), and lectures to be delivered at SIFTS 2019 (Madrid) and BUSSTEPP 2019 (Glasgow). v2: Fixed typos, added comments and references. v3. More references added and typos fixed
The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.
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.
The Euclidean path integral is well approximated by instantons. If instantons are dynamical, then instantons are necessarily complexified. These fuzzy instantons can have various physical applications. In slow-roll inflation models, fuzzy instantons can explain the probability distribution of the initial conditions of the universe. Even though the potential shape does not satisfy the slow-roll conditions following the swampland criteria, still the fuzzy instantons can explain the origin of the universe. If we extend the Euclidean path integral beyond the no-boundary proposal, we may study fuzz…
Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
Arnold-Sommerfeld Center for Theoretical Physics, Ludwig Maximilians Universität München（慕尼黑大学阿诺德-索末菲理论物理中心）；Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)（马克斯·普朗克物理研究所（维尔纳·海森堡研究所））；Institute for Theoretical Physics, Heidelberg University（海德堡大学理论物理研究所）；Niels Bohr International Academy, The Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；High Energy Physics Department, Institute for Mathematics, Astrophysics, and Particle Physics, Radboud University（拉德堡德大学数学、天体物理和粒子物理研究所高能物理系）
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.
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 co…
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…
Holography and the Swampland: Constraints on Quantum Gravity from Holographic Principles
Inter-University Centre for Astronomy and Astrophysics (IUCAA)（大学间天文学与天体物理学中心）；Department of Physics, K.L.S. College, Nawada, Magadh University（那达德KLS学院物理系，马加德大学）；Center for Theoretical Physics, Tomsk State Pedagogical University（托木斯克国立师范学院理论物理中心）；National Research Tomsk Polytechnic University（托木斯克理工大学国家研究型大学）；Núcleo Interdisciplinar de Ciências Exatas e da Natureza, NICEN, Universidade Federal de Pernambuco（伯南布哥联邦大学精确与自然科学跨学科核心）；Department of Nuclear Physics, Institute of Physics, University of São Paulo（圣保罗大学物理研究所核物理系）
In this contribution, we review a general argument showing that de Sitter critical points of extended supergravity are in tension with the magnetic weak gravity conjecture if the gravitino mass is vanishing. Motivated by this assumption, we review then the gravitino conjecture, which states that the limit of vanishing gravitino mass is pathological for the effective field theory description. Finally, we discuss more in general the fate of de Sitter critical points (with massless gravitini) in supergravity and comment on extensions of these works along various directions. Part of the material h…
The de Sitter Swampland conjecture compels us to consider dark energy models where $λ(ϕ) \equiv |\nabla_ϕ V|/V$ is bounded below by a positive constant. Moreover, it has been argued for Quintessence models that the constant $λ$ scenario is the least constrained. Here we demonstrate that increasing $λ$ only exacerbates existing tension in the Hubble constant $H_0$. The identification of dark energy models that both evade observational bounds and alleviate $H_0$ tension constitutes a robust test for the Swampland program.
In this article, we want to check four inflation models, such as composite NJL inflation (NJLI), Glueball inflation(GI), super Yang-Mills inflation (SYMI), and Orientifold inflation (OI), with two conjectures of the swampland program: scalar weak gravity conjecture (SWGC) and strong scalar weak gravity conjecture (SSWGC) since all these models violate the dS swampland conjecture(DSC) but are compatible with further refining de Sitter swampland conjecture (FRDSSC) through manual adjustment of free parameters of the mentioned conjecture. We want to study the simultaneous compatibility of each mo…
We show that constraints on scalar field potentials and towers of light massive states in asymptotic limits of scalar field space (as posited by the de Sitter Conjecture and the Swampland Distance Conjecture, respectively) are correlated with the prospects for defining asymptotic observables in expanding FRW cosmologies. The observations of a "census taker" in an eternally inflating cosmology are further related to the question of whether certain domain walls satisfy a version of the Weak Gravity Conjecture. This suggests that answers to fundamental questions about asymptotic observables in co…
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…
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 $R_{AdS}$, 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} \left( 1/\ln R_{A…
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.
From Frame Covariance to the Swampland Distance Conjecture
Institute of Physics, University of Tartu（塔尔图大学物理研究所）；School of Physics and Astronomy, University of Nottingham（诺丁汉大学物理与天文学学院）；Nottingham Centre of Gravity, University of Nottingham（诺丁汉大学引力中心）
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 review the advanced version of the KKLT construction and pure $d=4$ de Sitter supergravity, involving a nilpotent multiplet, with regard to various conjectures that de Sitter state cannot exist in string theory. We explain why we consider these conjectures problematic and not well motivated, and why the recently proposed alternative string theory models of dark energy, ignoring vacuum stabilization, are ruled out by cosmological observations at least at the $3σ$ level, i.e. with more than $99.7\%$ confidence.
Freezing Swampland: A Krylov Complexity Criterion for the Weak Gravity Conjecture
Sharif University of Technology（谢里夫理工大学）；Research Center for High Energy Physics, Department of Physics, Sharif University of Technology（谢里夫理工大学物理学院高能物理研究中心）
[Abridged] We realize the Agrawal-Obied-Vafa (AOV) swampland proposal of fading dark matter by the model of Salam-Sezgin and its string realization of Cvetic-Gibbons-Pope. The model describes a compactification of 6-dimensional supergravity with a monopole background on a 2-sphere. In 4 dimensions, there are 2 scalar fields, $X$ and $Y $, and the effective potential in the Einstein frame is an exponential with respect to $Y$ times a quadratic polynomial in the field $e^{-X}$. When making the volume of the 2-sphere large, namely for large values of $Y$, there appears a tower of states, which ac…
Motivated by principles from the Swampland program, which characterize requirements for a consistent UV completion of quantum gravity, combined with observational data, we are led to a unique corner of the quantum gravity landscape. In particular, using the Distance/Duality conjecture and the smallness of dark energy, we predict the existence of a light tower of states and a unique extra mesoscopic dimension of length $l\sim Λ^{-\frac{1}{4}}\sim 10^{-6}\, m$, with extra massless fermions propagating on it. This automatically leads to a candidate for a tower of sterile neutrinos, and an associa…
The Swampland Program aims to address the question, "when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?", and can be regarded as a bottom-up approach to investigations of quantum gravity. An alternative top-down approach aim to explore the imprints and the constraints imposed by the string theory dualities and symmetries on the effective field theory representations of quantum gravity. The most celebrated example of this approach is mirror symmetry. Mirror symmetry was first observed in worldsheet contructions of string compact…
Optimal paths across potentials on scalar field space
CUNEF Universidad（CUNEF大学）；Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)（马克斯·普朗克物理研究所（维尔纳·海森堡研究所））；Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilian-Universität（路德维希-马克西米利安大学阿诺德·索末菲理论物理中心）
Fundamental principles of local quantum field theory or of quantum gravity can enforce consistency requirements on the space of consistent low-energy effective field theories. We survey the various techniques that have been used to put UV constraints on IR physics, including those from causality considerations in the form of S-matrix positivity and bootstrap bounds, scattering time delays, conformal field theory and holographic methods, together with those that arise from landscape/swampland criteria such as the weak gravity conjecture. We review recent applications of these constraints to cor…
In this review we argue that four-dimensional effective field theory descriptions with de Sitter isometries are allowed in the presence of time-dependent internal degrees of freedom in type IIB string landscape. Both moduli stabilizations and time-independent Newton constants are possible in such backgrounds. However once the time-dependences are switched off, there appear no possibilities of effective field theory descriptions and these backgrounds are in the swampland.
The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead tower construction as a possible organising principle for the topological structures entering the formulation of the conjecture. We discuss why and how to include geometric structures in bordism groups, such as higher U(1)-bundles with connection. The inclusion of magnetic defects is also addressed in some detail. We further elaborate on how the conjecture co…
We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in $d>2$ spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithm…
