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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.
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H. Ooguri and T. Takayanagi, “Cobordism Conjecture in AdS,” arXiv:2006.13953 [hep-th]
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D. Gaiotto and X. Yin, “Notes on superconformal Chern-Simons-Matter theories,” JHEP
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2015
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M. Buican and T. Nishinaka, “Compact Conformal Manifolds,” JHEP
2015
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2015
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2016
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M. Montero, G. Shiu, and P. Soler, “The Weak Gravity Conjecture in three dimensions,” JHEP
2016
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2016
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2016
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2016
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C. Cordova, T. T. Dumitrescu, and K. Intriligator, “Deformations of Superconformal Theories,” JHEP
2016
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2016
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M. R. Gaberdiel and R. Gopakumar, “String Theory as a Higher Spin Theory,” JHEP
2016
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2017
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B. Heidenreich, M. Reece, and T. Rudelius, “Evidence for a sublattice weak gravity conjecture,” JHEP
2017
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M. Montero, “Are tiny gauge couplings out of the Swampland?,” JHEP
2017
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D. Klaewer and E. Palti, “Super-Planckian Spatial Field Variations and Quantum Gravity,” JHEP
2017
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2017
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D. Simmons-Duffin, “The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT,” JHEP
2017
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2017
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2017
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2017
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2017
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2018
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S.-J. Lee, W. Lerche, and T. Weigand, “Tensionless Strings and the Weak Gravity Conjecture,” JHEP
2018
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2018
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C. Behan, “Conformal manifolds: ODEs from OPEs,” JHEP
2018
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2018
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2018
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M. R. Gaberdiel and R. Gopakumar, “Tensionless string spectra on AdS 3
2018
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J.-B. Bae, S. Lee, and J. Song, “Modular Constraints on Superconformal Field Theories,” JHEP
2019
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D. Harlow and H. Ooguri, “Constraints on Symmetries from Holography,” Phys. Rev. Lett
2019
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M. Montero, “A Holographic Derivation of the Weak Gravity Conjecture,” JHEP
2019
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J. P. Conlon and F. Quevedo, “Putting the Boot into the Swampland,” JHEP
2019
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2019
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E. Gonzalo, L. E. Ibáñez, and Á. M. Uranga, “Modular Symmetries and the Swampland Conjectures,” JHEP
2019
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2019
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D. Meltzer, “Higher Spin ANEC and the Space of CFTs,” JHEP
2019
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2019
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2019
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