fermionic self-energy and the vertex correction both vanish, the result of a Ward identity. For $k\neq 0$, the fermion self-energy gives mass corrections, e.g. $\delta (1/m) = 8u/(15m) \times d\ell$ to leading order. Detailed analysis is given in the Supplementary Material. Given these calculations, we choose $z=2- 8u/15$ to keep the mass $m$ fixed, which gives the RG equations, to lowest order in $m/M_c, m/M_0$: $$\begin{aligned}
 \label{betaftn} %EG
&& \frac{d }{d \ell} u = \varepsilon \, u - \frac{30N_f+8}{15}
u^2, \\ 
&&  \frac{d}{d \ell}\left(\tfrac{m}{M_c}\right ) = -0.152 u
 \left(\tfrac{m}{M_c}\right) ,  \frac{d}{d \ell}\left(\tfrac{m}{M_0}\right ) = - \tfrac{8}{15}u 
 \left(\tfrac{m}{M_0}\right)  .\nonumber \end{aligned}$$

From the first equation above we find the fixed point coupling and hence dynamical exponent, $$u^* =  \frac{15}{30 N_f+8 } \varepsilon  
\, ,\,  z=2-\frac{4}{15 N_f+4 } \varepsilon ,$$ and since $u^*>0$, the second line in Eq.  implies both $m/M_0$ and $m/M_c$ are irrelevant. This establishes the existence and nature of the stable, isotropic fixed point describing the LAB phase. As a check, we have carried out a large $N_f$ expansion, which gives the same bosonic anomalous dimension as in the $\varepsilon$ expansion at the one-loop level, supporting the stability of the LAB phase.

The presence of the stable interacting fixed point 