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

Abstract

The emergence of a strongly coupled ultraviolet fixed point in lattice models that cross into the conformal window has long been hypothesized. The 4-dimensional 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 a 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 with discontinuity exponent ν = 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 Berezinsky-Kosterlitz-Thouless (BKT) scaling, though second order scaling cannot be excluded. BKT scaling would 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.

Symmetric Mass Generation

“…Numerical studies [144][145][146] of the (2 + 1)D su(4) SMG found η ∼ 1.05 and ν ∼ 1.30, which are close to the (large-N f limit) exponents (η = ν = 1) of the (2 + 1)D Gross-Neveu-Yukawa universality class [162,163]. Recent study [155] of the (3 + 1)D so(4) SMG also favors ν ∼ 1, although the result is not conclusive yet. However, the SMG mechanism is physically distinct from the symmetry-breaking mass generation described by the Gross-Neveu-Yukawa model.…”

“…Many different numerical methods have been used to study these models, which include the density matrix renormalization group (DMRG) [113], auxiliary-field quantum Monte Carlo (QMC) [143], hybrid Monte Carlo (HMC) [155,160], and fermion bag Monte Carlo (FBMC) [161].…”

“…The scaling analysis was performed mainly in (2 + 1)D systems, where the simulation can achieve a linear system size up to L = 60 [145], which enables a rather reliable estimate of critical exponents. As a comparison, for (3 + 1)D systems, the simulation can only reach L = 20 [155].…”

Dilaton Effective Field Theory

“…Lattice studies of SU(3) gauge theories with N f = 8 flavors of fundamental (Dirac) fermions [7][8][9][10][11][12][13], as well as N f = 2 flavors of symmetric two-index (Dirac) fermions (sextets) [14][15][16][17][18][19], have reported evidence for the presence of a surprisingly light flavorsinglet scalar particle in the accessible range of fermion masses. Motivated by the possibility that such a particle might be an approximate dilaton, we analyzed the lattice data in terms of an effective field theory (EFT) framework that extends the field content of a conventional chiral Lagrangian [20][21][22][23][24].…”

Composite two-Higgs doublet model from dilaton effective field theory

“…The resulting dilaton EFT has a long history, dating back at least to early studies of dynamical symmetry breaking [41][42][43] (see also Refs. [44][45][46]), but the recent lattice measurements have led to a resurgence of interest [47][48][49][50][51][52][53][54][55][56][57][58][59][60]. The application of the dilaton EFT to lattice data yields a parameter measurement [52,53] consistent with a large anomalous dimension for the bilinear fermion condensate [61][62][63][64].…”