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
N1 - Publisher Copyright:
© 2015 American Physical Society.
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.
UR - http://www.scopus.com/inward/record.url?scp=84922495861&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84922495861&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.91.045011
DO - 10.1103/PhysRevD.91.045011
M3 - Article
AN - SCOPUS:84922495861
SN - 1550-7998
VL - 91
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 4
M1 - 045011
ER -