Spontaneous Z2 Symmetry Breaking in the Orbifold Daughter of N=1 Super Yang-Mills Theory, Fractional Domain Walls and Vacuum Structure

TL;DR

This paper investigates the spontaneous breaking of Z2 symmetry in an orbifold gauge theory derived from supersymmetric Yang-Mills, revealing fractional domain walls and implications for nonperturbative equivalence and string theory connections.

Contribution

It demonstrates Z2 symmetry breaking in the orbifold daughter of N=1 SYM and introduces fractional domain walls, challenging assumptions about planar equivalence.

Findings

Z2 symmetry is spontaneously broken in the orbifold theory.

Existence of fractional domain walls similar to string theory D-branes.

Orbifold daughter is nonperturbatively nonequivalent to the parent SYM.

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 analyze dynamics of domain walls and argue that the Z2 symmetry is spontaneously broken. 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.