  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).
