Consistency of chiral symmetry breaking in chiral Yang-Mills theory with adiabatic continuity

We study the pattern of chiral symmetry breaking in the... model [with the chiral fermion sector containing.fijg,. 1/2 ij, and.Ai; see Armoni and Shifman Phys. Rev. D 85, 105003 (2012)] on R3 x S1 L and derive implications forcing R4 physics. Center-symmetric vacua are stabilized by a double-trace deformation. With the center symmetry maintained at small LoS1THORN <<.-1, i.e., at weak coupling, no phase transitions are expected in passing to large LoS1 THORN >>.-1 (here,. is the dynamical Yang-Mills scale). Starting with the small- L limit, we find the leading-order nonperturbative corrections in the given theory. The instanton-monopole operators induce the adjoint chiral condensate h.fijg. 1/2 jk i. 0 at weak coupling, i.e., at LoS1THORN <<.-1. Then adiabatic continuity tells us that h.fijg. 1/2 jki. 0 exists on R4, in full accord with the prediction from Bolognesi et al. [Phys. Rev. D 97, 094007 (2018)]. Simultaneously with h.fijg. 1/2 jki .3dik, the SUoNcTHORN gauge symmetry is spontaneously broken at strong coupling down to its maximal Abelian subgroup.