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We establish a precise relation between the modular bootstrap, used to constrain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry.
H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, and M. Viazovska, “Universal optimality of the
1902
Earlier work this paper cites.
1903
Earlier work this paper cites.
Y.-H. Lin and S.-H. Shao, “Anomalies and Bounds on Charged Operators,”
1904
Earlier work this paper cites.
1904
Earlier work this paper cites.
H. F. Blichfeldt, “The minimum value of quadratic forms, and the closest packing of spheres,”
1929
Earlier work this paper cites.
E. Hlawka, “Zur geometrie der zahlen,”
1943
Earlier work this paper cites.
P. Delsarte, “Bounds for unrestricted codes, by linear programming,”
1972
Earlier work this paper cites.
G. A. Kabatiansky and V. I. Levenshtein, “On bounds for packings on a sphere and in space,”
1978
Earlier work this paper cites.
V. Levenshtein, “Bounds for packings in
1979
Earlier work this paper cites.
A. M. Odlyzko and N. J. Sloane, “A theta-function identity for nonlattice packings,”
1980
Earlier work this paper cites.
J. D. Bekenstein, “Universal upper bound on the entropy-to-energy ratio for bounded systems,”
1981
Earlier work this paper cites.
No. 21. Cambridge University Press, 1983
T. M. Thompson, · 1983
Earlier work this paper cites.
I. B. Frenkel, J. Lepowsky, and A. Meurman, “A natural representation of the fischer-griess monster with the modular function j as character,”
1984
Earlier work this paper cites.
Springer-Verlag, Berlin, Heidelberg, 1987
J. H. Conway, N. J. A. Sloane, and E. Bannai, · 1987
Earlier work this paper cites.
D. V. Gorbachev, “Extremal problem for entire functions of exponential spherical type, connected with the levenshtein bound on the sphere packing density in
2000
Earlier work this paper cites.
O. Lunin and S. D. Mathur, “Correlation functions for M**N / S(N) orbifolds,”
2001
Earlier work this paper cites.
H. Cohn, “New upper bounds on sphere packings II,”
2002
Earlier work this paper cites.
H. Cohn, Y. Zhao,
2002
Earlier work this paper cites.
H. Cohn and N. Elkies, “New upper bounds on sphere packings I,”
2003
Earlier work this paper cites.
T. C. Hales, “A proof of the Kepler conjecture,”
2005
Earlier work this paper cites.
S. Torquato and F. H. Stillinger, “New conjectural lower bounds on the optimal density of sphere packings,”
2006
Earlier work this paper cites.
G. Parisi and F. Zamponi, “Amorphous packings of hard spheres for large space dimension,”
2006
Earlier work this paper cites.
N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, “The String landscape, black holes and gravity as the weakest force,”
2007
Earlier work this paper cites.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,”
2007
Earlier work this paper cites.
2007
Cited alongside, same era.
G. Höhn, “Conformal designs based on vertex operator algebras,”
2008
Cited alongside, same era.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,”
2008
Cited alongside, same era.
Springer Science & Business Media, 2008
C. Zong, · 2008
Cited alongside, same era.
Springer, 2008
D. Zagier, “Elliptic modular forms and their applications,” in · 2008
Cited alongside, same era.
H. Cohn and A. Kumar, “Optimality and uniqueness of the Leech lattice among lattices,”
D. de Laat and F. Vallentin, “A Breakthrough in Sphere Packing: The Search for Magic Functions,”
2016
Later among the works it cites.
T. Hartman, S. Jain, and S. Kundu, “Causality Constraints in Conformal Field Theory,”
2016
Later among the works it cites.
M. S. Viazovska, “The sphere packing problem in dimension 8,”
2017
Later among the works it cites.
H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, and M. Viazovska, “The sphere packing problem in dimension 24,”
2017
Later among the works it cites.
D. Mazac, “Analytic bounds and emergence of AdS
2017
Later among the works it cites.
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2009
Cited alongside, same era.
A. Maloney and E. Witten, “Quantum Gravity Partition Functions in Three Dimensions,”
2010
Cited alongside, same era.
G. Parisi and F. Zamponi, “Mean-field theory of hard sphere glasses and jamming,”
2010
Cited alongside, same era.
S. Hellerman, “A Universal Inequality for CFT and Quantum Gravity,”
2011
Cited alongside, same era.
M. S. Costa, V. Goncalves, and J. Penedones, “Conformal Regge theory,”
2012
Cited alongside, same era.
D. Friedan and C. A. Keller, “Constraints on 2d CFT partition functions,”
2013
Cited alongside, same era.
C. A. Keller and H. Ooguri, “Modular Constraints on Calabi-Yau Compactifications,”
2013
Cited alongside, same era.
2017
Later among the works it cites.
H. Cohn, “A conceptual breakthrough in sphere packing,”
2017
Later among the works it cites.
CRC Press, Boca Raton, FL, 2017
G. F. Tóth, “Packing and covering,” in · 2017
Later among the works it cites.
J. Qiao and S. Rychkov, “Cut-touching linear functionals in the conformal bootstrap,”
2017
Later among the works it cites.
S. Caron-Huot, “Analyticity in Spin in Conformal Theories,”
2017
Later among the works it cites.
J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, “Looking for a bulk point,”
2017
Later among the works it cites.
S. Collier, Y.-H. Lin, and X. Yin, “Modular Bootstrap Revisited,”
2018
Later among the works it cites.
E. Dyer, A. L. Fitzpatrick, and Y. Xin, “Constraints on Flavored 2d CFT Partition Functions,”
2018
Later among the works it cites.
A. Belin, A. Castro, J. Gomes, and C. A. Keller, “Siegel paramodular forms and sparseness in AdS
2018
Later among the works it cites.
T. Anous, R. Mahajan, and E. Shaghoulian, “Parity and the modular bootstrap,”
2018
Later among the works it cites.
2018
Later among the works it cites.
M. Viazovska, “Sharp sphere packings,”
2018
Later among the works it cites.
P. Kravchuk and D. Simmons-Duffin, “Light-ray operators in conformal field theory,”
2018
Later among the works it cites.
D. Mazac and M. F. Paulos, “The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices,”
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J.-B. Bae, S. Lee, and J. Song, “Modular Constraints on Superconformal Field Theories,”
2019
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