Built on

S. Ferrara, A. F. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
Earlier work this paper cites.
M.-C. Cha, M. P. A. Fisher, S. M. Girvin, M. Wallin, and A. P. Young, “Universal conductivity of two-dimensional films at the superconductor-insulator transition,” Phys. Rev. B
1991
Earlier work this paper cites.
H. Osborn and A. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Earlier work this paper cites.
A. C. Petkou, “C(T) and C(J) up to next-to-leading order in 1/N in the conformally invariant O(N) vector model for 2 < d < 4 2<d<4 ,” Phys.Lett
1995
Earlier work this paper cites.
A. Petkou, “Conserved currents, consistency relations and operator product expansions in the conformally invariant O(N) vector model,” Annals Phys
1996
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
2001
Earlier work this paper cites.
A. Pelissetto and E. Vicari, “Critical phenomena and renormalization-group theory,” Phys. Rept
2002
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
2002
Earlier work this paper cites.
J. Lipa, J. Nissen, D. Stricker, D. Swanson, and T. Chui, “Specific heat of liquid helium in zero gravity very near the lambda point,” Phys.Rev
2003
Earlier work this paper cites.
P. Calabrese and P. Parruccini, “Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach,” Phys.Rev
2005
Earlier work this paper cites.
J. Šmakov and E. Sørensen, “Universal scaling of the conductivity at the superfluid-insulator phase transition,” Phys. Rev. Lett
2005
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
2006
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, “Universal Constraints on Conformal Operator Dimensions,” Phys. Rev
Original
2009
Earlier work this paper cites.
I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully, “Holography from Conformal Field Theory,” JHEP
Original
2009
Earlier work this paper cites.
F. Caracciolo and V. S. Rychkov, “Rigorous Limits on the Interaction Strength in Quantum Field Theory,” Phys. Rev
Original
2010
Earlier work this paper cites.
I. Heemskerk and J. Sully, “More Holography from Conformal Field Theory,” JHEP
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
Original
2011
Cited alongside, same era.
R. Rattazzi, S. Rychkov, and A. Vichi, “Bounds in 4D Conformal Field Theories with Global Symmetry,” J. Phys
Original
2011
Cited alongside, same era.
A. Vichi, “Improved bounds for CFT’s with global symmetries,” JHEP
Original
2012
Cited alongside, same era.
D. Poland, D. Simmons-Duffin, and A. Vichi, “Carving Out the Space of 4D CFTs,” JHEP
Original
2012
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

Then

Y. Nakayama and T. Ohtsuki, “Five dimensional O ⁡ ( N ) O(N) -symmetric CFTs from conformal bootstrap,” Phys.Lett
Original
2014
Later among the works it cites.
S. M. Chester, J. Lee, S. S. Pufu, and R. Yacoby, “The 𝒩 = 8 \mathcal{N}=8 superconformal bootstrap in three dimensions,” JHEP
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
Original
2014
Later among the works it cites.
A. L. Fitzpatrick, J. Kaplan, and M. T. Walters, “Universality of Long-Distance AdS Physics from the CFT Bootstrap,” JHEP
Original
2014
Later among the works it cites.
F. Gliozzi and A. Rago, “Critical exponents of the 3d Ising and related models from Conformal Bootstrap,” JHEP

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2015

Bootstrapping the O(N) Archipelago

Kos, Filip, Poland, David, Simmons-Duffin, David et al.

Understand

We study 3d CFTs with an $O(N)$ global symmetry using the conformal bootstrap for a system of mixed correlators.

Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension $O(N)$ vector $\phi_i$ and the lowest dimension $O(N)$ singlet $s$, assumed to be the only relevant operators in their symmetry representations.
The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions $(\Delta_\phi, \Delta_s)$ to lie inside small islands.
We also make rigorous determinations of current two-point functions in the $O(2)$ and $O(3)$ models, with applications to transport in condensed matter systems.

Built on

S. Ferrara, A. F. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
Earlier work this paper cites.
M.-C. Cha, M. P. A. Fisher, S. M. Girvin, M. Wallin, and A. P. Young, “Universal conductivity of two-dimensional films at the superconductor-insulator transition,” Phys. Rev. B
1991
Earlier work this paper cites.
H. Osborn and A. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Earlier work this paper cites.
A. C. Petkou, “C(T) and C(J) up to next-to-leading order in 1/N in the conformally invariant O(N) vector model for 2 < d < 4 2<d<4 ,” Phys.Lett
1995
Earlier work this paper cites.
A. Petkou, “Conserved currents, consistency relations and operator product expansions in the conformally invariant O(N) vector model,” Annals Phys
1996
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
2001
Earlier work this paper cites.
A. Pelissetto and E. Vicari, “Critical phenomena and renormalization-group theory,” Phys. Rept
2002
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
2002
Earlier work this paper cites.
J. Lipa, J. Nissen, D. Stricker, D. Swanson, and T. Chui, “Specific heat of liquid helium in zero gravity very near the lambda point,” Phys.Rev
2003
Earlier work this paper cites.
P. Calabrese and P. Parruccini, “Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach,” Phys.Rev
2005
Earlier work this paper cites.
J. Šmakov and E. Sørensen, “Universal scaling of the conductivity at the superfluid-insulator phase transition,” Phys. Rev. Lett
2005
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
2006
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, “Universal Constraints on Conformal Operator Dimensions,” Phys. Rev
Original
2009
Earlier work this paper cites.
I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully, “Holography from Conformal Field Theory,” JHEP
Original
2009
Earlier work this paper cites.
F. Caracciolo and V. S. Rychkov, “Rigorous Limits on the Interaction Strength in Quantum Field Theory,” Phys. Rev
Original
2010
Earlier work this paper cites.
I. Heemskerk and J. Sully, “More Holography from Conformal Field Theory,” JHEP
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
Original
2011
Cited alongside, same era.
R. Rattazzi, S. Rychkov, and A. Vichi, “Bounds in 4D Conformal Field Theories with Global Symmetry,” J. Phys
Original
2011
Cited alongside, same era.
A. Vichi, “Improved bounds for CFT’s with global symmetries,” JHEP
Original
2012
Cited alongside, same era.
D. Poland, D. Simmons-Duffin, and A. Vichi, “Carving Out the Space of 4D CFTs,” JHEP
Original
2012
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

Then

Y. Nakayama and T. Ohtsuki, “Five dimensional O ⁡ ( N ) O(N) -symmetric CFTs from conformal bootstrap,” Phys.Lett
Original
2014
Later among the works it cites.
S. M. Chester, J. Lee, S. S. Pufu, and R. Yacoby, “The 𝒩 = 8 \mathcal{N}=8 superconformal bootstrap in three dimensions,” JHEP
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
Original
2014
Later among the works it cites.
A. L. Fitzpatrick, J. Kaplan, and M. T. Walters, “Universality of Long-Distance AdS Physics from the CFT Bootstrap,” JHEP
Original
2014
Later among the works it cites.
F. Gliozzi and A. Rago, “Critical exponents of the 3d Ising and related models from Conformal Bootstrap,” JHEP

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2012

Cited alongside, same era.

S. El-Showk and K. Papadodimas, “Emergent Spacetime and Holographic CFTs,” JHEP

Original

2012

Cited alongside, same era.

P. Liendo, L. Rastelli, and B. C. van Rees, “The Bootstrap Program for Boundary CFT d

Original

2013

Cited alongside, same era.

C. Beem, L. Rastelli, and B. C. van Rees, “The 𝒩 = 4 \mathcal{N}=4 Superconformal Bootstrap,” Phys.Rev.Lett

Original

2013

Cited alongside, same era.

A. L. Fitzpatrick, J. Kaplan, D. Poland, and D. Simmons-Duffin, “The Analytic Bootstrap and AdS Superhorizon Locality,” JHEP

Original

2013

Cited alongside, same era.

Z. Komargodski and A. Zhiboedov, “Convexity and Liberation at Large Spin,” JHEP

Original

2013

Cited alongside, same era.

S. El-Showk and M. F. Paulos, “Bootstrapping Conformal Field Theories with the Extremal Functional Method,” Phys.Rev.Lett

Original

2013

Cited alongside, same era.

F. Gliozzi, “More constraining conformal bootstrap,” Phys.Rev.Lett

Original

2013

Cited alongside, same era.

Original

2014