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

Abstract

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 - epsilon dimensions. This theory has cubic interaction terms 1/2g(1)sigma(phi(i))(2) + 1/6g(2)sigma(3). 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 epsilon(3). 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 Z(2) symmetry under phi -> -phi. 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.