The gradient flow in λϕ 4 theory

Abstract

Abstract: A gradient flow equation for λϕ4 theory in D = 4 is formulated. In this scheme the gradient flow equation is written in terms of the renormalized probe variable Φ(t, x) and renormalized parameters m2 and λ in a manner analogous to the higher derivative regularization. No extra divergence is induced in the interaction of the probe variable Φ(t, x) and the 4-dimensional dynamical variable ϕ(x) which is defined in renormalized perturbation theory. The finiteness to all orders in perturbation theory is established by power counting argument in the context of D + 1 dimensional field theory. This illustrates that one can formulate the gradient flow for the simple but important λϕ4 theory in addition to the well-known Yang-Mills flow, and it shows the generality of the gradient flow for a wider class of field theory.