Symmetric Mass Generation with four SU(2) doublet fermions

We study a single exactly massless staggered fermion in the fundamental representation of an $SU(2)$ gauge group. We utilize an nHYP-smeared fermion action supplemented with additional heavy Pauli-Villars fields which serve to decrease lattice artifacts. The phase diagram exhibits a clear two-phase structure with a conformal phase at weak coupling and a novel new phase, the Symmetric Mass Generation (SMG) phase, appearing at strong coupling. The SMG phase is confining with all states gapped and chiral symmetry unbroken. Our finite size scaling analysis provides strong evidence that the phase transition between these two phases is continuous, which would allow for the existence of a continuum SMG phase. Furthermore, the RG flows are consistent with a $\beta$-function that vanishes quadratically at the new fixed point suggesting that the $N_f=4$ flavor SU(2) gauge theory lies at the opening of the conformal window.