Built on

S. Ferrara, A. F. Grillo and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys. 76
1973
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.
R. Guida and J. Zinn-Justin, “Critical exponents of the N vector model,” J. Phys. A 31
1998
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
M. Hasenbusch, “Eliminating leading corrections to scaling in the three-dimensional O(N) symmetric phi**4 model: N=3 and N=4,” J. Phys. A 34
2001
Earlier work this paper cites.
M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi and E. Vicari, “Critical exponents and equation of state of the three-dimensional Heisenberg universality class,” Phys. Rev. B 65
2002
Earlier work this paper cites.
P. Calabrese, A. Pelissetto and E. Vicari, “Multicritical phenomena in O(n(1)) + O(n(2)) symmetric theories,” Phys. Rev. B 67
2003
Earlier work this paper cites.
J. Korevaar, “Tauberian theory: a century of development.” Springer, 2004. 497 pp
2004
Earlier work this paper cites.
M. Campostrini, M. Hasenbusch, A. Pelissetto and E. Vicari, “The Critical exponents of the superfluid transition in He-4,” Phys. Rev. B 74
2006
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP 0812
Original
2008
Earlier work this paper cites.
F. Caracciolo and V. S. Rychkov, “Rigorous Limits on the Interaction Strength in Quantum Field Theory,” Phys. Rev. D 81
Original
2010
Earlier work this paper cites.

Similar

R. Rattazzi, S. Rychkov and A. Vichi, “Central Charge Bounds in 4D Conformal Field Theory,” Phys. Rev. D 83
Original
2011
Cited alongside, same era.
R. Rattazzi, S. Rychkov and A. Vichi, “Bounds in 4D Conformal Field Theories with Global Symmetry,” J. Phys. A 44
Original
2011
Cited alongside, same era.
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
Original
2012
Cited alongside, same era.
D. Poland, D. Simmons-Duffin and A. Vichi, “Carving Out the Space of 4D CFTs,” JHEP 1205
Original
2012
Cited alongside, same era.
D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, “OPE Convergence in Conformal Field Theory,” Phys. Rev. D 86

Then

F. Kos, D. Poland and D. Simmons-Duffin, “Bootstrapping the O ⁡ ( n ) O(n) vector models,” JHEP 1406
Original
2014
Later among the works it cites.
F. Kos, D. Poland and D. Simmons-Duffin, “Bootstrapping Mixed Correlators in the 3D Ising Model,” JHEP 1411
Original
2014
Later among the works it cites.
F. Caracciolo, A. C. Echeverri, B. von Harling and M. Serone, “Bounds on OPE Coefficients in 4D Conformal Field Theories,” JHEP 1410
Original
2014
Later among the works it cites.
Y. Nakayama and T. Ohtsuki, “Approaching the conformal window of O ⁡ ( n ) × O ⁡ ( m ) O(n)\times O(m) symmetric Landau-Ginzburg models using the conformal bootstrap,” Phys. Rev. D 89
Original
2014
Later among the works it cites.
D. Simmons-Duffin, “A Semidefinite Program Solver for the Conformal Bootstrap,” JHEP 1506

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2016

The Effective Bootstrap

Echeverri, Alejandro Castedo, von Harling, Benedict, Serone, Marco

Understand

We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref.

[1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled.
In contrast to the most used method based on derivatives evaluated at the symmetric point $z=\bar z =1/2$, we can consistently "integrate out" higher-dimensional operators and get a reduced simpler, and faster to solve, set of bootstrap equations.
We test this "effective" bootstrap by studying the 3D Ising and $O(n)$ vector models and bounds on generic 4D CFTs, for which extensive results are already available in the literature.

Built on

S. Ferrara, A. F. Grillo and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys. 76
1973
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.
R. Guida and J. Zinn-Justin, “Critical exponents of the N vector model,” J. Phys. A 31
1998
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
M. Hasenbusch, “Eliminating leading corrections to scaling in the three-dimensional O(N) symmetric phi**4 model: N=3 and N=4,” J. Phys. A 34
2001
Earlier work this paper cites.
M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi and E. Vicari, “Critical exponents and equation of state of the three-dimensional Heisenberg universality class,” Phys. Rev. B 65
2002
Earlier work this paper cites.
P. Calabrese, A. Pelissetto and E. Vicari, “Multicritical phenomena in O(n(1)) + O(n(2)) symmetric theories,” Phys. Rev. B 67
2003
Earlier work this paper cites.
J. Korevaar, “Tauberian theory: a century of development.” Springer, 2004. 497 pp
2004
Earlier work this paper cites.
M. Campostrini, M. Hasenbusch, A. Pelissetto and E. Vicari, “The Critical exponents of the superfluid transition in He-4,” Phys. Rev. B 74
2006
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP 0812
Original
2008
Earlier work this paper cites.
F. Caracciolo and V. S. Rychkov, “Rigorous Limits on the Interaction Strength in Quantum Field Theory,” Phys. Rev. D 81
Original
2010
Earlier work this paper cites.