Dynamics of Simplest Chiral Gauge Theories

Abstract

Arguably, the simplest chiral gauge theories are $\mathrm{SO}(10)$ with $N_f$ fermion fields in the spinor representation {\bf 16}. We study their dynamics using their supersymmetric limits perturbed by an infinitesimal anomaly-mediated supersymmetry breaking as a guide. We predict the theory is gapped for $N_f=1,2$, while the $\mathrm{SU}(N_f)$ global symmetry is broken to $\mathrm{SO}(\mathrm{N}_f)$ for moderately large $N_f \geq 3$.

Figures (3)

• Figure 1: $N_f=2$ case, plot of the potential as a function of $v$ with $\Lambda=1$, without the anomaly mediation $m=0$ in blue, and with the anomaly mediation $m=0.01$ in red.
• Figure 2: $N_f=3$ case, Top: Contour plot of the potential on the $(\theta,\phi)$ plane with $\Lambda=1$, $m=0.01$, and $v$ at its minimum Eq. \ref{['eq:v3']}. It shows the minimum at $\phi=0$ and $\theta=\arctan\sqrt{2} \approx 0.955$. The other minimum is equivalent under $(\theta,\phi)\simeq(-\theta,-\phi)$. Bottom: The behavior of the potential along the $v$ direction with (red) and without (blue) the anomaly mediation.
• Figure 3: Contour plot of the potential on the $(H^+, \chi)$ plane with $M=0.01$, $m=0.0001$, $\Lambda=1$. The yellow cross is the location of the minimum. The region $\chi > \sqrt{2}H^+$ is cut off because it cannot satisfy the $D$-flatness condition Eq. \ref{['eq:Dflat']}.