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.
O. Nachtmann, “Positivity constraints for anomalous dimensions,” Nucl.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.
G. Mack, “Duality in Quantum Field Theory,” Nucl.Phys
1977
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.
N. Seiberg, “Electric - magnetic duality in supersymmetric nonAbelian gauge theories,” Nucl. Phys
1995
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.
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.
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.
M. Campostrini, M. Hasenbusch, A. Pelissetto, and E. Vicari, “The Critical exponents of the superfluid transition in He-4,” Phys.Rev
2006
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L. F. Alday and J. M. Maldacena, “Comments on operators with large spin,” JHEP
Original
2007
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R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
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V. S. Rychkov and A. Vichi, “Universal Constraints on Conformal Operator Dimensions,” Phys. Rev
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
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R. Rattazzi, S. Rychkov, and A. Vichi, “Central Charge Bounds in 4D Conformal Field Theory,” Phys. Rev
Original
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Earlier work this paper cites.
R. Rattazzi, S. Rychkov, and A. Vichi, “Bounds in 4D Conformal Field Theories with Global Symmetry,” J. Phys
Original
2011
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A. Vichi, “Improved bounds for CFT’s with global symmetries,” JHEP
Original
2012
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D. Poland, D. Simmons-Duffin, and A. Vichi, “Carving Out the Space of 4D CFTs,” JHEP
Original
2012
Earlier work this paper 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
Original
2012
Earlier work this paper cites.
D. Poland and D. Simmons-Duffin, “N=1 SQCD and the Transverse Field Ising Model,” JHEP
Original
2012
Earlier work this paper cites.
P. Liendo, L. Rastelli, and B. C. van Rees, “The Bootstrap Program for Boundary CFT d
Original
2013
Earlier work this paper cites.

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2015

Non-Abelian Binding Energies from the Lightcone Bootstrap

Li, Daliang, Meltzer, David, Poland, David

Understand

We analytically study the lightcone limit of the conformal bootstrap for 4-point functions containing scalars charged under global symmetries.

We show the existence of large spin double-twist operators in various representations of the global symmetry group.
We then compute their anomalous dimensions in terms of the central charge $C_T$, current central charge $C_J$, and the OPE coefficients of low dimension scalars.
In AdS, these results correspond to the binding energy of two-particle states arising from the exchange of gravitons, gauge bosons, and light scalar fields.

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.
O. Nachtmann, “Positivity constraints for anomalous dimensions,” Nucl.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.
G. Mack, “Duality in Quantum Field Theory,” Nucl.Phys
1977
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.
N. Seiberg, “Electric - magnetic duality in supersymmetric nonAbelian gauge theories,” Nucl. Phys
1995
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.
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.
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.
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.
L. F. Alday and J. M. Maldacena, “Comments on operators with large spin,” JHEP
Original
2007
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.
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.
R. Rattazzi, S. Rychkov, and A. Vichi, “Central Charge Bounds in 4D Conformal Field Theory,” Phys. Rev
Original
2011
Earlier work this paper cites.
R. Rattazzi, S. Rychkov, and A. Vichi, “Bounds in 4D Conformal Field Theories with Global Symmetry,” J. Phys
Original
2011
Earlier work this paper cites.
A. Vichi, “Improved bounds for CFT’s with global symmetries,” JHEP
Original
2012
Earlier work this paper cites.
D. Poland, D. Simmons-Duffin, and A. Vichi, “Carving Out the Space of 4D CFTs,” JHEP
Original
2012
Earlier work this paper 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
Original
2012
Earlier work this paper cites.
D. Poland and D. Simmons-Duffin, “N=1 SQCD and the Transverse Field Ising Model,” JHEP
Original
2012
Earlier work this paper cites.
P. Liendo, L. Rastelli, and B. C. van Rees, “The Bootstrap Program for Boundary CFT d
Original
2013
Earlier work this paper cites.