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We consider QCD-like theories with one massless fermion in variousrepresentations of the gauge group SU$(N)$. The theories are formulated on$R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all thesetheories are characterized by confinement, mass gap and spontaneous breaking ofa (discrete) chiral symmetry ($\chi$SB). At small $r(S_1)$, in order tostabilize the vacua of these theories at a center-symmetric point, we suggestto perform a double trace deformation. With these deformation, the theories athand are at weak coupling at small $r(S_1)$ and yet exhibit basic features ofthe large-$r(S_1)$ limit: confinement and $\chi$SB. We calculate the stringtension, mass gap, bifermion condensates and $\theta$ dependence. Thedouble-trace deformation becomes dynamically irrelevant at large $r(S_1)$.Despite the fact that at small $r(S_1)$ confinement is Abelian, while it isexpected to be non-Abelian at large $r(S_1)$, we argue that small andlarge-$r(S_1)$ physics are continuously connected. If so, one can usesmall-$r(S_1)$ laboratory to extract lessons about QCD and QCD-like theories on$R_4$.

QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations