Critical O(2) field theory near six dimensions beyond one loop

A tensorial representation of phi(4) field theory introduced by Herbut and Janssen [Phys. Rev. D 93, 085005 (2016)] is studied close to six dimensions, with an eye towards a possible realization of an interacting conformal field theory in five dimensions. We employ the two-loop e expansion, two-loop fixed-dimension renormalization group, and nonperturbative functional renormalization group. An interacting, real, infrared-stable fixed point is found near six dimensions, and the corresponding anomalous dimensions are computed to the second order in the small parameter epsilon = 6 - d. Two-loop epsilon expansion indicates, however, that the second-order corrections may destabilize the fixed point at some critical epsilon(c) < 1. A more detailed analysis within all three computational schemes suggests that the interacting, infrared-stable fixed point found previously collides with another fixed point and becomes complex when the dimension is lowered from six towards five. Such a result would conform to the expectation of the triviality of O(2) field theories above four dimensions.