Functional renormalization group approach to dipolar fixed point which is scale invariant but nonconformal

A dipolar fixed point introduced by Aharony and Fisher is a physical example of interacting scale-invariant but nonconformal field theories. We find that the perturbative critical exponents computed in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ε</a:mi></a:math> expansions violate the conformal bootstrap bound. We formulate the functional renormalization group equations 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). Published by the American Physical Society 2024