Four loop renormalization of ϕ3 theory in six dimensions

We renormalize six-dimensional ϕ³ theory in the modified minimal subtraction (MS ¯ ) scheme at four loops. From the resulting β -function, anomalous dimension, and mass anomalous dimension, we compute four loop critical exponents relevant to the Lee-Yang edge singularity and percolation problems. Using resummation methods and information on the exponents of the relevant two-dimensional conformal field theory, we obtain estimates for exponents in dimensions 3, 4, and 5 which are in reasonable agreement with other techniques for these two problems. The renormalization group functions for the more general theory with an O (N ) symmetry are also computed in order to obtain estimates of exponents at various fixed points in five dimensions. Included in this O (N ) analysis is the full evaluation of the mass operator mixing matrix of anomalous dimensions at four loops. We show that its eigenexponents are in agreement with the mass exponents computed at O (1 /N²) in the nonperturbative large N expansion.