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M. Fujiwara, Über die obere Schranke des absoluten Betrages der Wurzeln einer algebraischen Gleichung , Tôhoku Math J 10: 167–171 (1916)
1916
Earlier work this paper cites.
A. M. Polyakov, Conformal symmetry of critical fluctuations , JETP Lett. 12, 381 (1970) [Pisma Zh. Eksp. Teor. Fiz. 12, 538 (1970)]
1970
Earlier work this paper cites.
A. A. Migdal, Conformal invariance and bootstrap , Phys. Lett. B 37, 386 (1971)
1971
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory , Zh. Eksp. Teor. Fiz. 66, 23 (1974)
1974
Earlier work this paper cites.
J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories , Nucl. Phys. B 270, 186 (1986)
1986
Earlier work this paper cites.
G. W. Moore and N. Seiberg, Classical and Quantum Conformal Field Theory , Commun. Math. Phys. 123, 177 (1989)
1989
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, Phys. Rev. Lett. 69 (1992) 1849 [arXiv:9204099 [hep-th]]
1992
Earlier work this paper cites.

Similar

M. Banados, M. Henneaux, C. Teitelboim, and J. Zanelli, Phys. Rev. D 48 (1993) 1506 [arXiv:9302012 [gr-qc]]
1993
Cited alongside, same era.
G. Höhn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster , Ph.D. thesis (Bonn 1995), Bonner Mathematische Schriften 286 (1996), 1-85, [arXiv:0706.0236]
Original
1996
Cited alongside, same era.
E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:9802150 [hep-th]]
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A. Strominger, Black hole entropy from near-horizon microstates , JHEP02 (1998) 009
1998
Cited alongside, same era.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B 599, 459 (2001) [arXiv:0011040 [hep-th]]
2001
Cited alongside, same era.

Then

M. R. Gaberdiel, Constraints on extremal self-dual CFTs , JHEP 0711, 087 (2007) hep-th/0707.4073
Original
2007
Later among the works it cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 0812, 031 (2008) [arXiv:0807.0004 [hep-th]]
Original
2008
Later among the works it cites.
V. S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions , Phys. Rev. D 80.4 (2009): 045006 [arXiv:0905.2211 [hep-th]]
Original
2009
Later among the works it cites.
S. Hellerman, A Universal Inequality for CFT and Quantum Gravity , JHEP 08 (2011) 130 [arXiv:0902.2790v2 [hep-th]]
Original
2011
Later among the works it cites.
S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin, and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap , Phys. Rev. D 86.2 (2012): 025022 [arXiv:1203.6064 [hep-th]]

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2013

Bounds on Operator Dimensions in 2D Conformal Field Theories

Qualls, Joshua D., Shapere, Alfred D.

Understand

We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $\Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators.

The bound we find is of the same form as found for $\Delta_1$: $\Delta_2 \leq c_{tot}/12 + O(1)$.
We find a similar bound on the conformal dimension $\Delta_3$, and present a method for deriving bounds on $\Delta_n$ for any $n$, under slightly modified assumptions.
For asymptotically large $c_{tot}$ and fixed $n$, we show that $\Delta_n \leq \frac{c_{tot}}{12}+O(1)$.

Built on

M. Fujiwara, Über die obere Schranke des absoluten Betrages der Wurzeln einer algebraischen Gleichung , Tôhoku Math J 10: 167–171 (1916)
1916
Earlier work this paper cites.
A. M. Polyakov, Conformal symmetry of critical fluctuations , JETP Lett. 12, 381 (1970) [Pisma Zh. Eksp. Teor. Fiz. 12, 538 (1970)]
1970
Earlier work this paper cites.
A. A. Migdal, Conformal invariance and bootstrap , Phys. Lett. B 37, 386 (1971)
1971
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory , Zh. Eksp. Teor. Fiz. 66, 23 (1974)
1974
Earlier work this paper cites.
J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories , Nucl. Phys. B 270, 186 (1986)
1986
Earlier work this paper cites.
G. W. Moore and N. Seiberg, Classical and Quantum Conformal Field Theory , Commun. Math. Phys. 123, 177 (1989)
1989
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, Phys. Rev. Lett. 69 (1992) 1849 [arXiv:9204099 [hep-th]]
1992
Earlier work this paper cites.

Similar

M. Banados, M. Henneaux, C. Teitelboim, and J. Zanelli, Phys. Rev. D 48 (1993) 1506 [arXiv:9302012 [gr-qc]]
1993
Cited alongside, same era.
G. Höhn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster , Ph.D. thesis (Bonn 1995), Bonner Mathematische Schriften 286 (1996), 1-85, [arXiv:0706.0236]
Original
1996
Cited alongside, same era.
E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:9802150 [hep-th]]
1998
Cited alongside, same era.
A. Strominger, Black hole entropy from near-horizon microstates , JHEP02 (1998) 009
1998
Cited alongside, same era.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B 599, 459 (2001) [arXiv:0011040 [hep-th]]
2001
Cited alongside, same era.