SpontaneousZ2symmetry breaking in the orbifold daughter ofN=1super-Yang-Mills theory, fractional domain walls and vacuum structure

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Abstract
We discuss the fate of the Z2 symmetry and the vacuum structure in an SU(N)xSU(N) gauge theory with one bifundamental Dirac fermion. This theory can be obtained from SU(2N) supersymmetric Yang--Mills (SYM) theory by virtue of Z2 orbifolding. We use a variety of interrelated techniques to prove that the Z2 symmetry is spontaneously broken. Our arguments are mostly field-theoretic; they are based on (i) matching (or, better to say, mismatching) of the gravitational chiral anomaly; (ii) analysis of domain walls in the parent and daughter theories; (iii) low-energy theorems related to the scale anomaly. Since unbroken Z2 is a necessary condition for nonperturbative planar equivalence we conclude that the orbifold daughter is nonperturbatively nonequivalent to its supersymmetric parent. En route, our investigation reveals the existence of fractional domain walls, similar to fractional D-branes of string theory on orbifolds. We conjecture on the fate of these domain walls in the true solution of the Z2-broken orbifold theory. We also comment on relation with nonsupersymmetric string theories and closed-string tachyon condensation