Indications of isotropic Lifshitz points in four dimensions

TL;DR

This paper investigates the existence of isotropic Lifshitz points in a four-dimensional U(1) scalar theory using the Functional Renormalization Group, revealing a line of Lifshitz points with properties similar to the BKT phase.

Contribution

It provides the first indication of a line of Lifshitz points in four dimensions through a novel RG analysis with a specific truncation scheme.

Findings

Indications of a line of Lifshitz points in 4D scalar theory.

Similarities to the Berezinsky-Kosterlitz-Thouless phase.

Evidence of algebraic decay of correlations at certain parameters.

Abstract

The presence of isotropic Lifshitz points for a U(1) symmetric scalar theory is investigated with the help of the Functional Renormalization Group at the conjectured lower critical dimension d=4. To this aim, a suitable truncation in the expansion of the effective action in powers of the field is considered and, consequently, the Renormalization Group flow is reduced to a set of ordinary differential equations for the parameters that define the effective action. Within this approximation, indications of a line of Lifshitz points are found, that present evident similarities with the properties shown by the line of fixed points observed in the two dimensional Berezinsky-Kosterlitz-Thouless phase. In particular, this line of Lifshitz points exhibits the vanishing of the expectation value of the field, together with a finite stiffness and, for specific combinations of the parameters that define the effective action, also the algebraic decay at large distance of the order parameter correlations.