TY - JOUR

T1 - Three loop analysis of the critical O (N) models in 6-ε dimensions

AU - Fei, Lin

AU - Giombi, Simone

AU - Klebanov, Igor R.

AU - Tarnopolsky, Grigory

PY - 2015/2/10

Y1 - 2015/2/10

N2 - We continue the study, initiated in [L. Fei, S. Giombi, and I.R. Klebanov, Phys. Rev. D 90, 025018 (2014)], of the O(N) symmetric theory of N+1 massless scalar fields in 6-ε dimensions. This theory has cubic interaction terms 12g1σ(φi)2+16g2σ3. We calculate the three loop beta functions for the two couplings and use them to determine certain operator scaling dimensions at the IR stable fixed point up to order ε3. We also use the beta functions to determine the corrections to the critical value of N below which there is no fixed point at real couplings. The result suggests a significant reduction in the critical value as the dimension is decreased to 5. We also study the theory with N=1, which has a Z2 symmetry under φ→-φ. We show that it possesses an IR stable fixed point at imaginary couplings which can be reached by flow from a nearby fixed point describing a pair of N=0 theories. We calculate certain operator scaling dimensions at the IR fixed point of the N=1 theory and suggest that, upon continuation to two dimensions, it describes a nonunitary conformal minimal model.

AB - We continue the study, initiated in [L. Fei, S. Giombi, and I.R. Klebanov, Phys. Rev. D 90, 025018 (2014)], of the O(N) symmetric theory of N+1 massless scalar fields in 6-ε dimensions. This theory has cubic interaction terms 12g1σ(φi)2+16g2σ3. We calculate the three loop beta functions for the two couplings and use them to determine certain operator scaling dimensions at the IR stable fixed point up to order ε3. We also use the beta functions to determine the corrections to the critical value of N below which there is no fixed point at real couplings. The result suggests a significant reduction in the critical value as the dimension is decreased to 5. We also study the theory with N=1, which has a Z2 symmetry under φ→-φ. We show that it possesses an IR stable fixed point at imaginary couplings which can be reached by flow from a nearby fixed point describing a pair of N=0 theories. We calculate certain operator scaling dimensions at the IR fixed point of the N=1 theory and suggest that, upon continuation to two dimensions, it describes a nonunitary conformal minimal model.

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U2 - 10.1103/PhysRevD.91.045011

DO - 10.1103/PhysRevD.91.045011

M3 - Article

AN - SCOPUS:84922495861

VL - 91

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

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

SN - 1550-7998

IS - 4

M1 - 045011

ER -