Asymptotic Safety Guaranteed in Supersymmetry

We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, $R$ charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the $a$ theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories.

Figure 1

Phase space for asymptotic safety, showing the parameter regions (10) and (11). Models in the gray-shaded area are UV incomplete. The $P$ axis is scaled as $P/(1-P)$ for better display. The full dot indicates the example in Figs. 2 and 3.

Figure 2

Phase diagram with asymptotic safety for supersymmetry ($P=-5$, $R=(3/2)$, $\epsilon =(1/1000)$; Fig. 1) projected onto ${\alpha }_y=({\alpha }_1+{\alpha }_2)/2$. Trajectories are pointing towards the IR. Notice that ${\alpha }_1$ is destabilized and asymptotic freedom is absent. Dots show the Gaussian, the UV, and the IR fixed points. Also shown are separatrices (red) and sample trajectories (gray).

Figure 3

The running couplings ${\alpha }_i(t)$ in units of RG time $t=\ln (\mu /\mathrm{\Lambda })$ along the separatrix from the UV to the IR fixed point. Parameters are as in Fig. 2. All couplings in units of ${\alpha }_{2,\mathrm{UV}}^{*}$ with $t_{\mathrm{tr}}=\ln ({\mu }_{\mathrm{tr}}/\mathrm{\Lambda })$ and $\mathrm{\Lambda }$ the high scale; see (13).