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We introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity.
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L. van den Dries, Tame topology and o-minimal structures , vol. 248 of London Mathematical Society Lecture Note Series . Cambridge University Press, Cambridge, 1998, 10.1017/CBO9780511525919
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M. Kneser, Quadratische Formen . Springer-Verlag, Berlin, 2002, 10.1007/978-3-642-56380-5
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M. R. Douglas, The Statistics of string / M theory vacua , JHEP 05
2003
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M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua , Commun. Math. Phys. 252
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T. W. Grimm and J. Louis, The Effective action of N = 1 Calabi-Yau orientifolds , Nucl. Phys. B 699
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F. Denef and M. R. Douglas, Distributions of nonsupersymmetric flux vacua , JHEP 03
2005
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M. Graña, Flux compactifications in string theory: A Comprehensive review , Phys. Rept. 423
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V. Kumar and W. Taylor, String Universality in Six Dimensions , Adv. Theor. Math. Phys. 15
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T. W. Grimm, The N=1 effective action of F-theory compactifications , Nucl. Phys. B845
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D. S. Park and W. Taylor, Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry , JHEP 01
2012
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M. Dierigl and J. J. Heckman, Swampland cobordism conjecture and non-Abelian duality groups , Phys. Rev. D 103
2012
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Z. Lu and M. R. Douglas, Gauss-Bonnet-Chern theorem on moduli space , Math. Ann. 357
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M. R. Douglas, Spaces of Quantum Field Theories , J. Phys. Conf. Ser. 462
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Cited alongside, same era.
M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics , J. Diff. Geom. 72
2006
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M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua. III. String/M models , Commun. Math. Phys. 265
2006
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J. Pila and A. J. Wilkie, The rational points of a definable set , Duke Mathematical Journal 133
2006
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A. Font, B. Fraiman, M. Graña, C. A. Núñez and H. P. De Freitas, Exploring the landscape of heterotic strings on T d T^{d} , JHEP 10
2007
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M. R. Douglas and S. Kachru, Flux compactification , Rev. Mod. Phys. 79
2007
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H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland , Nucl. Phys. B766
2007
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2013
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T. W. Grimm, T. G. Pugh and M. Weissenbacher, The effective action of warped M-theory reductions with higher-derivative terms - Part II , JHEP 12
2015
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T. W. Grimm, T. G. Pugh and M. Weissenbacher, The effective action of warped M-theory reductions with higher derivative terms — part I , JHEP 01
2016
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D. Harlow, Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture , JHEP 01
2016
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B. Heidenreich, M. Reece and T. Rudelius, The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff , Eur. Phys. J. C 78
2018
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T. W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States , JHEP 08
2018
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B. Heidenreich, M. Reece and T. Rudelius, Emergence of Weak Coupling at Large Distance in Quantum Gravity , Phys. Rev. Lett. 121
2018
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B. Bakker, Hodge theory and o-minimality , Notes from the Felix Klein lecture series in Bonn (2019)
2019
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P. Corvilain, T. W. Grimm and I. Valenzuela, The Swampland Distance Conjecture for Kähler moduli , JHEP 08
2019
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B. Bakker, B. Klingler and J. Tsimerman, Tame topology of arithmetic quotients and algebraicity of Hodge loci , J. Amer. Math. Soc. 33
2020
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S. Cecotti, Swampland geometry and the gauge couplings , JHEP 09
2021
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Y. Hamada and C. Vafa, 8d supergravity, reconstruction of internal geometry and the Swampland , JHEP 06
2021
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B. Bakker and S. Mullane, Definable structures on flat bundles , in preparation (2021)
2021
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