We show that recently proposed linear sigma models with torsion can be obtained from unconventional branches of conventional gauge theories. This observation puts models with log interactions on firm footing. If non-anomalous multiplets are integrated out, the resulting low-energy theory involves log interactions of neutral fields. For these cases, we find a sigma model geometry which is both non-toric and includes brane sources. These are heterotic sigma models with branes. Surprisingly, there are massive models with compact complex non-Kähler target spaces, which include brane/anti-brane sources. The simplest conformal models describe wrapped heterotic NS5-branes. We present examples of both types. © SISSA 2012.