$\mathcal{N}=1$ duality in the chiral limit from $\mathcal{N}=2$ duality

We study a deformation of $\mathcal{N}=2$ supersymmetric QCD with a $U(N)$ gauge group and $N_f$ number of quark flavors induced by the mass term $\mu$ for the adjoint matter which breaks supersymmetry down to $\mathcal{N}=1$ QCD. Recently this deformation was shown to lead to a weakly coupled dual theory only in two particular sets of vacua: the $r=N$ vacuum and the so-called zero vacua which can be found at $r<N_f-N$, where $r$ is the number of condensed quarks. For small quark masses and intermediate values of $\mu$, the gauge group of the dual theory is $U(N_f-N)\times U(1{)}^{2N-N_f}$, where the Abelian sector is heavy and can be integrated out. However, at larger values of $\mu$, the Abelian sector enters the strong coupling regime. We show that the ’t Hooft matching conditions in the chiral limit require the Seiberg neutral meson field $M$ from this sector to become light. In the $r=N$ vacuum, $M$ is constructed of a monopole and an antimonopole connected by confining magnetic strings, while in the zero vacua, it is built of a quark and antiquark connected by confining electric strings.

Figure 1

Meson formed by a monopole-antimonopole pair connected by two strings. Open and closed circles denote the monopole and antimonopole, respectively.