$\theta$ and the ${\eta }^{\prime }$ in Large $N$ Supersymmetric QCD

Abstract

We study the large $N$ $\theta$ dependence and the ${\eta }^{\prime }$ potential in supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in SUSY QCD are found to reflect a variety of expectations from large $N$ perturbation theory, including the presence of branches and the behavior of theories with matter (both with $N_f\ll N$ and $N_f\sim N$). However, there are also striking departures from ordinary QCD and the conventional large $N$ description: instanton effects, when under control, are not exponentially suppressed at large $N$, and branched structure in supersymmetric QCD is always associated with approximate discrete symmetries. We suggest that these differences motivate further study of large $N$ QCD on the lattice.

arXiv comment20 pages; v2: references updated; v3: expanded introduction, accepted for publication in JHEP

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