Built on

S. Ferrara, A. 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 THE QUANTUM FIELD THEORY AT SMALL DISTANCES,” Zh.Eksp.Teor.Fiz
1974
Earlier work this paper cites.
A. Vasiliev, Y. Pismak, and Y. Khonkonen, “1/N EXPANSION: CALCULATION OF THE EXPONENT ETA IN THE ORDER 1/N**3 BY THE CONFORMAL BOOTSTRAP METHOD,” Theor.Math.Phys
1982
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 0(N) vector model for 2 < d < 4 2<d<4 ,” Phys.Lett
1995
Earlier work this paper cites.
I. Klebanov and A. Polyakov, “AdS dual of the critical O(N) vector model,” Phys.Lett
2002
Earlier work this paper cites.
J. A. Gracey, “Crossover exponent in O(N) ϕ 4 {\phi}^{4} theory at O ⁡ ( 1 / N 2 CLOSE O(1/N^{2} ),” Phys.Rev.E
2002
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.

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2014

Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap

Nakayama, Yu, Ohtsuki, Tomoki

Understand

We investigate the conformal bootstrap approach to $O(N)$ symmetric CFTs in five dimension with particular emphasis on the lower bound on the current central charge.

The bound has a local minimum for all $N>1$, and in the large $N$ limit we propose that the minimum is saturated by the critical $O(N)$ vector model at the UV fixed point, the existence of which has been recently argued by Fei, Giombi, and Klebanov.
The location of the minimum is generically different from the minimum of the lower bound of the energy-momentum tensor central charge when it exists for smaller $N$.
To better understand the situation, we examine the lower bounds of the current central charge of $O(N)$ symmetric CFTs in three dimension to compare.

Built on

S. Ferrara, A. 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 THE QUANTUM FIELD THEORY AT SMALL DISTANCES,” Zh.Eksp.Teor.Fiz
1974
Earlier work this paper cites.
A. Vasiliev, Y. Pismak, and Y. Khonkonen, “1/N EXPANSION: CALCULATION OF THE EXPONENT ETA IN THE ORDER 1/N**3 BY THE CONFORMAL BOOTSTRAP METHOD,” Theor.Math.Phys
1982
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 0(N) vector model for 2 < d < 4 2<d<4 ,” Phys.Lett
1995
Earlier work this paper cites.
I. Klebanov and A. Polyakov, “AdS dual of the critical O(N) vector model,” Phys.Lett
2002
Earlier work this paper cites.
J. A. Gracey, “Crossover exponent in O(N) ϕ 4 {\phi}^{4} theory at O ⁡ ( 1 / N 2 CLOSE O(1/N^{2} ),” Phys.Rev.E
2002
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.