Analytical Derivation of Chiral Symmetry Breaking in QCD-like SU(N) and Sp(N) Gauge Theories using AMSB

We present an analytical derivation of the chiral symmetry breaking minima in supersymmetric asymptotically-free SU(N) and Sp(N) gauge theories with F flavors of “quarks”, perturbed by Anomaly-Mediated Supersymmetry Breaking. Applying AMSB to the ADS, quantum-modified, s-confining, free magnetic and conformal phases of these theories, we are able to show that almost all of them possess stable chiral symmetry breaking minima that could plausibly be continuously connected to the vacua of QCD-like SU(N) or Sp(N) theories in the complete SUSY breaking limit. These are exact results in the non-perturbative regime, and we treat SUSY purely as a theoretical tool.

In softly broken SU(N) SQCD, tachyonic two-loop AMSB masses for dual squarks induce baryonic runaways to incalculable global minima at the upper end of the free magnetic window (1.43N ≤ F ≤ 1.5N), while for the s-confining phase (F = N + 1) and most of the free-magnetic phase (F ≤ 1.43N) we find that naive tree-level baryonic runaways are stabilized by loop effects near the origin of moduli space. In these cases, we are able to only derive local SU(F)_L × SU(F)_R → SU(F)_V chiral symmetry breaking minima [arXiv:2212.03260 & 2111.09690]. However, in the Sp(N) counterparts, all the global minima have SU(2F) → Sp(F) breaking and are calculable. There are no tree-level runaways as baryons are absent, and directions with tachyonic dual squarks are naturally stabilized (to give local minima) by quartic tree-level SUSY potentials.