Non-Trivial Fixed Points of the Scalar Field Theory

TL;DR

This paper investigates the phase structure of a scalar field theory with complex potentials using the renormalization group, discovering many fixed points that are likely not physically viable due to unbounded actions.

Contribution

It derives the RG equation for the generating function and identifies numerous non-trivial fixed points in the theory's phase space.

Findings

Found infinitely many non-trivial fixed points.

Effective actions are unbounded from below.

Fixed points likely do not correspond to physical theories.

Abstract

The phase structure of the scalar field theory with arbitrary powers of the gradient operator and a local non-analytic potential is investigated by the help of the RG in Euclidean space. The RG equation for the generating function of the derivative part of the action is derived. Infinitely many non-trivial fixed points of the RG transformations are found. The corresponding effective actions are unbounded from below and do probably not exhibit any particle content. Therefore they do not provide physically sensible theories.