The gradient flow in $\lambda {\varphi }^4$ theory

Abstract

A gradient flow equation for $\lambda {\varphi }^4$ theory in $D=4$ is formulated. In this scheme the gradient flow equation is written in terms of the renormalized probe variable $\Phi (t,x)$ and renormalized parameters $m^2$ and $\lambda$ in a manner analogous to the higher derivative regularization. No extra divergence is induced in the interaction of the probe variable $\Phi (t,x)$ and the 4-dimensional dynamical variable $\varphi (x)$ 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 $\lambda {\varphi }^4$ 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.

22 pages. To appear in JHEP

References in corpus (2)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators

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