Scale-invariance and scale-breaking in parity-invariant three-dimensional QCD

We present a numerical study of three-dimensional two-color QCD with $N=0, 2, 4, 8$ and 12 flavors of massless two-component fermions using parity-preserving improved Wilson-Dirac fermions. A finite volume analysis provides strong evidence for the presence of $Sp(N)$ symmetry-breaking bilinear condensate when $N \le 2$ and its absence for $N \ge 8$. A weaker evidence for the bilinear condensate is shown for $N=4$. We estimate the critical number of flavors below which scale-invariance is broken by the bilinear condensate to be between $N=4$ and 6.