Functional renormalization group approach to dipolar fixed point which is scale-invariant but non-conformal

TL;DR

This paper investigates a dipolar fixed point that exhibits scale invariance without conformal invariance, using functional renormalization group methods to analyze its properties and critical exponents.

Contribution

It applies the functional renormalization group approach to a known non-conformal scale-invariant fixed point, providing new insights into its critical behavior.

Findings

Perturbative critical exponents violate conformal bootstrap bounds.

Functional RG equations are formulated and applied to study the fixed point.

Results in three dimensions are obtained within local potential approximations.

Abstract

A dipolar fixed point introduced by Aharony and Fisher is a physical example of interacting scale-invariant but non-conformal field theories. We find that the perturbative critical exponents computed in $\epsilon$ expansions violate the conformal bootstrap bound. We formulate the functional renormalization group equations a la Wetterich and Polchinski to study the fixed point. We present some results in three dimensions within (uncontrolled) local potential approximations (with or without perturbative anomalous dimensions).