Emergent strongly coupled ultraviolet fixed point in four dimensions with eight Kähler-Dirac fermions
Anna Hasenfratz
Abstract
The existence of a strongly coupled ultraviolet fixed point in four-dimensional lattice models as they cross into the conformal window has long been hypothesized. The SU(3) gauge system with eight fundamental fermions is a good candidate to study this phenomenon as it is expected to be very close to the opening of the conformal window. I study the system using staggered lattice fermions in the chiral limit. My numerical simulations employ improved lattice actions that include heavy Pauli-Villars (PV) type bosons. This modification does not affect the infrared dynamics but greatly reduces the ultraviolet fluctuations, thus allowing the study of stronger renormalized couplings than previously possible. I consider two different PV actions and find that both show an apparent continuous phase transition in the eight-flavor system. I investigate the critical behavior using finite size scaling of the renormalized gradient flow coupling. The finite size scaling curve-collapse analysis predicts a first-order phase transition consistent with discontinuity exponent $\ensuremath{\nu}=1/4$ in the system without PV bosons. The scaling analysis with the PV boson actions is not consistent with a first-order phase transition. The numerical data are well described by ``walking scaling'' corresponding to a renormalization group $\ensuremath{\beta}$ function that just touches zero, $\ensuremath{\beta}({g}^{2})\ensuremath{\sim}({g}^{2}\ensuremath{-}{g}_{\ensuremath{\star}}^{2}{)}^{2}$, though second-order scaling cannot be excluded. Walking scaling could imply that the eight-flavor system is the opening of the conformal window, an exciting possibility that could be related to 't Hooft anomaly cancellation of the system.