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Register a new userThe Swampland: Introduction and Review
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Authors
Eran Palti
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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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We study aspects of anti-de Sitter space in the context of the Swampland. In particular, we conjecture that the near-flat limit of pure AdS belongs to the Swampland, as it is necessarily accompanied by an infinite tower of light states. The mass of the tower is power-law in the cosmological constant, with a power of $frac{1}{2}$ for the supersymmetric case. We discuss relations between this behaviour and other Swampland conjectures such as the censorship of an unbounded number of massless fields, and the refined de Sitter conjecture. Moreover, we propose that changes to the AdS radius have an interpretation in terms of a generalised distance conjecture which associates a distance to variations of all fields. In this framework, we argue that the distance to the $Lambda rightarrow 0$ limit of AdS is infinite, leading to the light tower of states. We also discuss implications of the conjecture for de Sitter 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 uplifting, which is not affected by flattening. We show that this scenario is compatible with the weak gravity conjecture for a broad choice of parameters of the KL model. Thus, the results of our analysis do not support the recent swampland conjecture.
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. The weak gravity conjecture (WGC) for scalar potentials is saturated in the supercritical string scenarios discussed in this work, but only if one uses the dilaton as appears in the string effective action, with a kinetic term that is not canonically normalised. In the case of a non-critical Starobinsky potential, the WGC is satisfied by both the canonically-normalised dilaton and the dilaton used in the string effective action.
We consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass scale of an infinite tower of states, signalling the breakdown of the effective theory. The cutoff can be understood as the Weak Gravity Conjecture applied to the Stuckelberg gauge field in the mass term of the high spin fields. A strong version of our conjecture applies even if the graviton itself is massive, so to massive gravity. We provide further evidence for the conjecture from string theory.
We analyze four-dimensional Friedmann-Lemaitre-Robertson-Walker cosmologies in type IIB, arising from a M-theory dual, and find that the null energy condition (NEC) has to be obeyed by them (except for the negatively curved case) in order for the M-theory action to have a Wilsonian effective description. However, this does not imply that the M-theory metric has to obey the 11d NEC. Thus, we propose a new swampland conjecture -- the 4d NEC is a consistency condition for any theory to have a completion within M-theory -- with an explicit derivation of it for cosmological backgrounds from a top-down perspective. We briefly discuss the cosmological consequences of such a condition derived from M-theory.
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