TL;DR: In this article, a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian, which leads to evidence for a conjectured property of quantum gravity that there must exist an infinite tower of states whose mass decreases as an exponential function of the field variation.
Abstract: We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which allows us to apply the Weak Gravity Conjecture to such configurations. We show that this leads to evidence for a conjectured property of quantum gravity that as a scalar field variation in field space asymptotes to infinity there must exist an infinite tower of states whose mass decreases as an exponential function of the scalar field variation. We determine the rate at which the mass of the states reaches this exponential behaviour showing that it occurs quickly after the field variation passes the Planck scale.
TL;DR: The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot as mentioned in this paper, assuming only a knowledge of quantum field theory and general relativity.
Abstract: 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.
TL;DR: In this paper, the authors present a thorough review of recent Hubble constant estimates and a summary of the proposed theoretical solutions, including early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity.
Abstract: The $\Lambda$CDM model provides a good fit to a large span of cosmological data but harbors areas of phenomenology. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the $4-6\sigma$ disagreement between predictions of the Hubble constant $H_0$ by early time probes with $\Lambda$CDM model, and a number of late time, model-independent determinations of $H_0$ from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demand a hypothesis with enough rigor to explain multiple observations--whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. We present a thorough review of the problem, including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions. Some of the models presented are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within $1-2\sigma$ between {\it Planck} 2018, using CMB power spectra data, BAO, Pantheon SN data, and R20, the latest SH0ES Team measurement of the Hubble constant ($H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68\% confidence level). Reduced tension might not simply come from a change in $H_0$ but also from an increase in its uncertainty due to degeneracy with additional physics, pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.[Abridged]
TL;DR: The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot as mentioned in this paper, assuming only a knowledge of quantum field theory and general relativity.
Abstract: 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.
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Cites background from "Super-Planckian spatial field varia..."
...n interesting way to probe a gravitational censorship of large eld variations. The relation between the censorship of large spatial eld variations and the Swampland Distance Conjecture was studied in [9], while its relation to the axionic Weak Gravity Conjecture was studied in [155], and more generally to censorship of large eld variations in [156]. A more precise version of the above estimate on a b...
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... a U(1) gauge symmetry. In such cases, if the gauge coupling of the U(1) depends on a scalar eld ˚then the scalar eld will develop a spatial gradient which can support a trans-Planckian variation. In [9] such solutions were studied and it was argued that far away from the source, the gauge coupling g(˚) is of similar magnitude to the energy density in the scalar eld kinetic terms. Then the exponentia...
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...ximum variation ˚is obtained for a logarithmic spatial prole ˚˘logr, where ris the radial coordinate. A similar logarithmic bound was shown also for a general class of strongly curved backgrounds in [9]. An interesting implication of these results is that for super-Planckian spatial variations the energy density in the eld due to the kinetic terms ˆ, has to vary at least exponentially ˆ˘e ˚, for som...
TL;DR: In this paper, the authors test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory and show that such a limit must be located at infinite distance in the moduli space.
Abstract: We test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we analyze the limit in Kahler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. We show that such a limit must be located at infinite distance in the moduli space. As expected, the low-energy effective theory breaks down in this limit due to a tower of charged particles becoming massless. These are the excitations of an asymptotically tensionless string, which is shown to coincide with a critical heterotic string compactified to six dimensions. For a more quantitative analysis, we focus on a U(1) gauge symmetry and use a chain of dualities and mirror symmetry to determine the elliptic genus of the nearly tensionless string, which is given in terms of certain meromorphic weak Jacobi forms. Their modular properties in turn allow us to determine the charge-to-mass ratios of certain string excitations near the tensionless limit. We then provide evidence that the tower of asymptotically massless charged states satisfies the (sub-)Lattice Weak Gravity Conjecture, the Completeness Conjecture, and the Swampland Distance Conjecture. Quite remarkably, we find that the number theoretic properties of the elliptic genus conspire with the balance of gravitational and scalar forces of extremal black holes, such as to produce a narrowly tuned charge spectrum of superextremal states. As a byproduct, we show how to compute elliptic genera of both critical and non-critical strings, when refined by Mordell-Weil U(1) symmetries in F-theory.
TL;DR: In this paper, it has been shown that for a large class of points in moduli space the monodromy matrix generates an infinite orbit within the spectrum of BPS states, which can be used to identify an infinite tower of states with this orbit.
Abstract: It has been conjectured that in theories consistent with quantum gravity infinite distances in field space coincide with an infinite tower of states becoming massless exponentially fast in the proper field distance. The complex-structure moduli space of Calabi-Yau manifolds is a good testing ground for this conjecture since it is known to encode quantum gravity physics. We study infinite distances in this setting and present new evidence for the above conjecture. Points in moduli space which are at infinite proper distance along any path are characterised by an infinite order monodromy matrix. We utilise the nilpotent orbit theorem to show that for a large class of such points the monodromy matrix generates an infinite orbit within the spectrum of BPS states. We identify an infinite tower of states with this orbit. Further, the theorem gives the local metric on the moduli space which can be used to show that the mass of the states decreases exponentially fast upon approaching the point. We also propose a reason for why infinite distances are related to infinite towers of states. Specifically, we present evidence that the infinite distance itself is an emergent quantum phenomenon induced by integrating out at one-loop the states that become massless. Concretely, we show that the behaviour of the field space metric upon approaching infinite distance can be recovered from integrating out the BPS states. Similarly, at infinite distance the gauge couplings of closed-string Abelian gauge symmetries vanish in a way which can be matched onto integrating out the infinite tower of charged BPS states. This presents evidence towards the idea that also the gauge theory weak-coupling limit can be thought of as emergent.
TL;DR: In this paper, an upper bound on the strength of gravity relative to gauge forces in quantum gravity was given, motivated by arguments involving holography and absence of remnants, the stability of black holes as well as the non-existence of global symmetries in string theory.
Abstract: We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U(1) gauge field with gauge coupling g, there is a new ultraviolet scale Λ = gMPl, invisible to the low-energy effective field theorist, which sets a cutoff on the validity of the effective theory. Moreover, there is some light charged particle with mass smaller than or equal to Λ. The bound is motivated by arguments involving holography and absence of remnants, the (in) stability of black holes as well as the non-existence of global symmetries in string theory. A sharp form of the conjecture is that there are always light ``elementary'' electric and magnetic objects with a mass/charge ratio smaller than the corresponding ratio for macroscopic extremal black holes, allowing extremal black holes to decay. This conjecture is supported by a number of non-trivial examples in string theory. It implies the necessary presence of new physics beneath the Planck scale, not far from the GUT scale, and explains why some apparently natural models of inflation resist an embedding in string theory.
TL;DR: In this paper, the authors make a number of conjectures about the geometry of continuous moduli parameterizing the string landscape, including 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.
TL;DR: In this article, the authors discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetsries, and show that all continuous and continuous gauge symmetry are compact and all charges allowed by Dirac quantization are present in the spectrum.
Abstract: We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of Zp gauge theories shows that they are associated with an emergent Zp one-form (KalbRamond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear σ-models. It also allows us to expand on Polchinski’s classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.
TL;DR: In this article, the authors 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.
Abstract: 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 quantum gravitational theories. We propose certain finiteness criteria as one relevant factor in identifying this boundary (based on talks given at the Einstein Symposium in Alexandria, at the 2005 Simons Workshop in Mathematics and Physics, and the talk to have been presented at Strings 2005).
TL;DR: The weak gravity conjecture is generalized to product gauge groups and its tension with the naturalness principle for a charged scalar coupled to gravity is studied.
Abstract: The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge q and mass m with q>m/m_(Pl). We generalize the WGC to product gauge groups and study its tension with the naturalness principle for a charged scalar coupled to gravity. Reconciling naturalness with the WGC either requires a Higgs phase or a low cutoff at Λ∼qm_(Pl). If neither applies, one can construct simple models that forbid a natural electroweak scale and whose observation would rule out the naturalness principle.