Supersymmetric quantum chromodynamics (SQCD)

Supersymmetric quantum chromodynamics is an N=1 supersymmetric $SU(N_c)$ gauge theory with $N_f$ fundamental and $N_f$ antifundamental chiral multiplets.

The supersymmetric conformal window is the range of flavor numbers for which an asymptotically free supersymmetric gauge theory flows to an interacting infrared fixed point. Its lower edge is often detected when a gauge-invariant chiral operator reaches the scalar unitarity bound.

The chiral ring is generated by gauge-invariant chiral operators modulo relations that vanish by F-term equations. In SQCD its basic generators are meson and baryon operators.

An SQCD meson is the gauge-invariant chiral bilinear $M^i{}_j={\tilde{Q}}_j{Q}^i$. It transforms under both flavor groups and parametrizes mesonic directions of the vacuum moduli space.

An SQCD baryon contracts $N_c$ fundamental fields with the gauge epsilon tensor; an antibaryon similarly contracts antifundamentals. Such operators exist when enough flavors are available and obey relations with the mesons.

The holomorphic strong-coupling scale packages the gauge coupling and theta angle into ${\Lambda }^{b_0}$. Treating it as a spurion under anomalous chiral symmetries strongly constrains nonperturbative superpotentials and moduli-space deformations.

For SQCD with $N_f<N_c$, strong dynamics generates the Affleck–Dine–Seiberg superpotential. For $SU(2)$ with one flavor it is proportional to ${\Lambda }^5/M$ and produces a runaway to infinite meson expectation value.

When $N_f=N_c$, SQCD has no generated superpotential but its classical constraint is shifted by the strong-coupling scale. For $SU(2)$ with two flavors, one convention gives $\det M-B\tilde{B}={\Lambda }^4$.

A theory s-confines when its infrared physics is described smoothly everywhere on moduli space by gauge-invariant composites with a local superpotential and no remaining gauge group. SQCD with $N_f=N_c+1$ is the standard example.

Seiberg duality states that two different N=1 supersymmetric gauge theories flow to the same infrared quantum field theory. Gauge-invariant operators, global symmetries, 't Hooft anomalies and deformations match even though the ultraviolet gauge groups and elementary fields differ.