AMSB in $Sp(N_c)$ Gauge Theories

TL;DR

This work analyzes AMSB perturbations of $Sp(N_c)$ SQCD across its phase diagram, showing that stable chiral symmetry breaking minima exist for $N_f<3(N_c+1)$ and are plausibly connected to non-SUSY QCD vacua. The authors systematically study ADS-type, quantum-modified, s-confining, free magnetic, and conformal window regimes, employing electric, magnetic, and twice-dual descriptions to reveal where runaways are lifted and where the global minima reside, often on fully mesonic branches. A key result is that, even near the Banks–Zaks fixed points at both lower and upper conformal edges, AMSB deformations drive the theory toward chiral symmetry breaking minima, with the mesonic branch frequently providing the global minimum. These findings bolster the phenomenological relevance of AMSB-perturbed SUSY QCD for modeling QCD-like vacua and illustrate how dualities help constrain IR dynamics in softly broken theories.

Abstract

We present a careful study of the chiral symmetry breaking minima and other potential minima in supersymmetric symplectic QCD ($Sp(N_c)$ with $N_f$ flavors) perturbed by Anomaly Mediated Supersymmetry Breaking (AMSB). Although the case of $N_f = N_c +1$ requires particular care due to the inherently strongly coupled nature of the quantum modified moduli space, we are able to show that all $Sp(N_c)$ theories to which AMSB can be applied ($N_f < 3(N_c + 1)$) possess stable chiral symmetry breaking minima, which are plausibly continuously connected to the vacua of QCD-like $Sp(N_c)$ theories for large SUSY breaking, and are protected from runaways to incalculable minima.

Figures (8)

• Figure 1: The potential (in $\Lambda=1$ units) for the case $N_f=N_c+1=3$, with Kähler potential $K=\sqrt{1+\mathop{\mathrm{Tr}}\nolimits{M^\dagger M}}$ which properly interpolates between the small- and large-field regimes and maintains positive-definite kinetic terms everywhere. The red dot indicates the meson point, which can be seen to remain the global minimum of the theory. We parametrize the moduli as in \ref{['eq:Meson flavor class']} with $a_3 = \frac{2}{a_1a_2}$ to satisfy the quantum modified constraint.
• Figure 2: A plot for $N_f = 330$, $N_c = 230$, i.e. $N_f = 1.429(N_c+1)$. Couplings clearly flow to the fixed point (0, 0) along a straight-line trajectory. The red line is a plot of $m_{q}^{2} = 0$ and indeed the trajectory converges onto it near (0, 0). The region below the green line satisfies $m_{M}^{2} > 0$; the trajectory completely lies in this region.
• Figure 3: A 3D plot and a contour plot of the scalar potential in the upper end of the free magnetic phase $1.43(N_c + 1) < N_f < 1.5(N_c + 1)$ when the dual squarks are tachyonic and the meson mass-squared is positive. Both the dual squark VEV $\phi_q$ and the meson VEV $\phi_M$ are non-zero at the unique minimum. For these plots, we have assigned the numerical values $\widetilde{N_c} = 6$, $N_f = 22$ and $\frac{m}{\widetilde{\Lambda}} = 0.1$. The value of the scalar potential at the minimum is $-1.0305 \times 10^{-13}$ in units where $\widetilde{\Lambda} = 1$.
• Figure 4: Two-dimensional RGE flow of coupling constants near the magnetic Banks--Zaks fixed point (blue dot) with $N_f = 151$, $\widetilde{N}_c=50$. $m_{\widetilde{q}}^2 > 0$ below the red line, while $m_M^2 > 0$ below the green line.
• Figure 5: Above: Running of $g^2$ (red) and $\lambda^2$ (green), with the initial condition $g^2 = 0.2$, $\lambda^2 = \frac{1}{7} g^2 + 0.00015$, while the dashed lines show their infrared fixed point values. We took $N_{c} = 99$, $N_f=151$, $\widetilde{N}_c=50$, and hence $\epsilon \approx 0.0132$. Below: Corresponding running of $m_q^2$ (red) and $m_M^2$ (green) in units with $m=1$.