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1. Trans-Planckian Censorship and the Swampland

   Bedroya, Alek; Vafa, Cumrun (September 2019, ArXivorg)

   In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. Applied to the case of scalar fields, it leads to conditions that are similar to the refined dS Swampland conjecture. For large field ranges, TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges. In particular for asymptotic regions of field space, TCC leads to a bound |V′|≥2(d−1)(d−2)√V, which is consistent with all known cases in string theory. Like the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but it does allow sufficiently short-lived ones. 

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2. Pure supersymmetric AdS and the Swampland

   https://doi.org/10.1007/JHEP01(2023)094  

   Montero, Miguel; Roček, Martin; Vafa, Cumrun (January 2023, Journal of High Energy Physics)

   A bstract We point out that pure supergravity theories in AdS with enough supersymmetry lead, upon taking the large radius limit, to flat space quantum gravities with a nonperturbatively exact global symmetry, and are therefore in the Swampland. The argument applies to any AdS supergravity with gauged R-symmetry group, including truncations of most well known examples, such as AdS 5 without the S 5 or AdS 4 without the S 7 . This demonstrates that extreme scale separation, at least with enough supersymmetry, is not realizable. Moreover pure AdS theories are also in conflict with some other Swampland principles including the Weak Gravity Conjecture and the (generalized) Distance Conjecture. 

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3. Cobordism Classes and the Swampland

   McNamara, Jake; Vafa, Cumrun (September 2019, ArXivorg)

   We argue that any proposed quantum theory of gravity with non-trivial cobordism classes in the space of configurations belongs to the Swampland. The argument is based on the assumption that there are no global symmetries in a consistent theory of quantum gravity. The triviality of the cobordism classes requires the existence of certain stringy defects that trivialize the potential cobordism classes. We provide evidence for this conjecture by identifying those defects demanded by this argument that could preserve supersymmetry, and predict the existence of new non-supersymmetric defects in string theory. 

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4. Taxonomy of infinite distance limits

   https://doi.org/10.1007/JHEP03(2025)213  

   Etheredge, Muldrow; Heidenreich, Ben; Rudelius, Tom; Ruiz, Ignacio; Valenzuela, Irene (March 2025, Journal of High Energy Physics)

   The Emergent String Conjecture constrains the possible types of light towers in infinite-distance limits in quantum gravity moduli spaces. In this paper, we use these constraints to restrict the geometry of the scalar charge-to-mass vectors -∇ log m of the light towers and the analogous vector -∇ log Λ of the species scale. We derive taxonomic rules that these vectors must satisfy in each duality frame. Under certain assumptions, this allows us to classify the ways in which different duality frames can fit together globally in the moduli space in terms of a finite list of polytopes. Many of these polytopes arise in known string theory compactifications, while others suggest either undiscovered corners of the landscape or new swampland constraints. 

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5. Baby Universes, Holography, and the Swampland

   McNamara, Jacob; Vafa, Cumrun (April 2020, ArXivorg)

   On the basis of a number of Swampland conditions, we argue that the Hilbert space of baby universe states must be one-dimensional in a consistent theory of quantum gravity. This scenario may be interpreted as a type of “Gauss’s law for entropy” in quantum gravity, and provides a clean synthesis of the tension between Euclidean wormholes and a standard interpretation of the holographic dictionary, with no need for an ensemble. Our perspective relies crucially on the recently-proposed potential for quantum-mechanical gauge redundancies between states of the universe with different topologies. We further comment on the possible exceptions in d ≤ 3 for this hypothesis and the role of an ensemble in holographic theories in the context of theories of quantum gravity in d = 2 (such as JT gravity and possible cousins in d = 3), which we argue are incomplete physical theories that should be viewed as branes in a higher dimensional theory of quantum gravity for which an ensemble plays no role. 

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