Journey from Small to Large r(S1) with Double-Trace Deformations

We consider QCD-like theories with one massless fermion in various representations of the gauge group SU(N). The theories are formulated on R3 ×S1. In the decompactification limit of large r(S1) all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry (χSB). At small r(S1), in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small r(S1) and yet exhibit basic features of the large-r(S1) limit: confinement and χSB. We calculate the string tension, mass gap, bifermion condensates and θ dependence. The double-trace deformation becomes dynamically irrelevant at large r(S1). Despite the fact that at small r(S1) confinement is Abelian, while it is expected to be non-Abelian at large r(S1), we argue that small and large-r(S1) physics are continuously connected. If so, one can use small-r(S1) laboratory to extract lessons about QCD and QCD-like theories on R4.