TY - JOUR

T1 - Bootstrapping O (N) vector models in 4<d<6

AU - Chester, Shai M.

AU - Pufu, Silviu S.

AU - Yacoby, Ran

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/4/27

Y1 - 2015/4/27

N2 - We use the conformal bootstrap to study conformal field theories with O(N) global symmetry in d=5 and d=5.95 space-time dimensions that have a scalar operator φi transforming as an O(N) vector. The crossing symmetry of the four-point function of this O(N) vector operator, along with unitarity assumptions, determines constraints on the scaling dimensions of conformal primary operators in the φi×φj operator product expansion̄mposing a lower bound on the second smallest scaling dimension of such an O(N)-singlet conformal primary, and varying the scaling dimension of the lowest one, we obtain an allowed region that exhibits a kink located very close to the interacting O(N)-symmetric conformal field theory conjectured to exist recently by Fei, Giombi, and Klebanov. Under reasonable assumptions on the dimension of the second lowest O(N) singlet in the φi×φj operator product expansion, we observe that this kink disappears in d=5 for small enough N, suggesting that in this case an interacting O(N) conformal field theory may cease to exist for N below a certain critical value.

AB - We use the conformal bootstrap to study conformal field theories with O(N) global symmetry in d=5 and d=5.95 space-time dimensions that have a scalar operator φi transforming as an O(N) vector. The crossing symmetry of the four-point function of this O(N) vector operator, along with unitarity assumptions, determines constraints on the scaling dimensions of conformal primary operators in the φi×φj operator product expansion̄mposing a lower bound on the second smallest scaling dimension of such an O(N)-singlet conformal primary, and varying the scaling dimension of the lowest one, we obtain an allowed region that exhibits a kink located very close to the interacting O(N)-symmetric conformal field theory conjectured to exist recently by Fei, Giombi, and Klebanov. Under reasonable assumptions on the dimension of the second lowest O(N) singlet in the φi×φj operator product expansion, we observe that this kink disappears in d=5 for small enough N, suggesting that in this case an interacting O(N) conformal field theory may cease to exist for N below a certain critical value.

UR - http://www.scopus.com/inward/record.url?scp=84929179244&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929179244&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.91.086014

DO - 10.1103/PhysRevD.91.086014

M3 - Article

AN - SCOPUS:84929179244

SN - 1550-7998

VL - 91

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 8

M1 - 086014

ER -