RG flow of 4d Nonlinear Sigma model with $SU(n)$ target space

Let's consider the 4d Nonlinear Sigma model with $SU(n)$ target space, without a topological term. The Lagrangian is $\frac{f^2}{16}\mathrm{Tr}(\partial_{\mu}U^{-1} \partial^{\mu}U)$ where $U$ is a $SU(n)$ matrix, and $f$ is a coupling constant. Dimensional analysis shows $f$ has mass dimension 1. This means under RG, $f$ will grow. I am puzzled what happens when we flow to deep infrared? Does it flow to a gapless fixed point with spontaneously symmetry breaking, and if so is it a CFT? Or does it flow to a gapped fixed point?