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We give a short overview over recent work on finding constraints on partition functions of 2d CFTs from modular invariance.
Alexander M. Polyakov, Conformal symmetry of critical fluctuations , JETP Lett. 12
1970
Earlier work this paper cites.
Alexander A. Migdal, Conformal invariance and bootstrap , Phys.Lett. B37
1971
Earlier work this paper cites.
A.M. Polyakov, Nonhamiltonian approach to conformal quantum field theory , Zh.Eksp.Teor.Fiz. 66
1974
Earlier work this paper cites.
Peter Bouwknegt, EXTENDED CONFORMAL ALGEBRAS , Phys.Lett. B207
1988
Earlier work this paper cites.
Gregory W. Moore and Nathan Seiberg, Classical and Quantum Conformal Field Theory , Commun.Math.Phys. 123
1989
Earlier work this paper cites.
Satoru Odake, Extension of N = 2 N=2 Superconformal Algebra and Calabi-yau Compactification , Mod.Phys.Lett. A4
1989
Earlier work this paper cites.
by same author, C = 3- d d Conformal Algebra With Extended Supersymmetry , Mod.Phys.Lett. A5
1990
Earlier work this paper cites.
Maximo Banados, Claudio Teitelboim, and Jorge Zanelli, The Black hole in three-dimensional space-time , Phys.Rev.Lett. 69
1992
Cited alongside, same era.
Toshiya Kawai, Yasuhiko Yamada, and Sung-Kil Yang, Elliptic genera and N=2 superconformal field theory , Nucl.Phys. B414
1994
Cited alongside, same era.
S.-T. Yau, Review of geometry and analysis , Asian J. Math. 4
2000
Cited alongside, same era.
Edward Witten, Three-Dimensional Gravity Revisited , (2007)
2007
Cited alongside, same era.
Riccardo Rattazzi, Vyacheslav S. Rychkov, Erik Tonni, and Alessandro Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 0812
2008
Cited alongside, same era.
Sheer El-Showk and Miguel F. Paulos, Bootstrapping Conformal Field Theories with the Extremal Functional Method , (2012)
2012
Later among the works it cites.
Daniel Friedan, Anatoly Konechny, and Cornelius Schmidt-Colinet, Lower bound on the entropy of boundaries and junctions in 1+1d quantum critical systems , Phys.Rev.Lett. 109
2012
Later among the works it cites.
Daniel Friedan and Christoph A. Keller, Constraints on 2d CFT partition functions , JHEP 1310
2013
Closest in time.
by same author, Precise lower bound on Monster brane boundary entropy , JHEP 1307
2013
Closest in time.
Christoph A. Keller and Hirosi Ooguri, Modular Constraints on Calabi-Yau Compactifications , Commun.Math.Phys. 324
2013
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M. Fukuda K. Nakata M. Yamashita, K. Fujisawa and M. Nakata, A high-performance software package for semidefinite programs: SDPA 7 , Research Report B-463, Dept. of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, Japan, September 2010
2010
Cited alongside, same era.
Simeon Hellerman, A Universal Inequality for CFT and Quantum Gravity , JHEP 1108
2011
Cited alongside, same era.
Joshua D. Qualls and Alfred Shapere, Bounds on Operator Dimensions in 2D Conformal Field Theories , (2013)
2013
Closest in time.