Emergent strongly coupled ultraviolet fixed point in four dimensions with 8 Kähler-Dirac fermions

Abstract

The existence of a strongly coupled ultraviolet fixed point in 4-dimensional lattice models as they cross into the conformal window has long been hypothesized. The SU(3) gauge system with 8 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 8-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 $\nu =1/4$ 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 $\beta$ function that just touches zero, $\beta (g^2)\sim (g^2-g_{\star }^2{)}^2$, though second order scaling cannot be excluded. Walking scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that could be related to t'Hooft anomaly cancellation of the system.

arXiv commentVersion to be published in Phys. Rev. D. Contains significant new numerical data and streamlined analysis. 12 pages, 8 figures

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• Gradient flow step-scaling function for SU(3) with $N_f=8$ fundamental flavors
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