Bootstrap bound for conformal multi-flavor QCD on lattice

Abstract

The recent work by Iha et al. shows an upper bound on mass anomalous dimension γm of multi-flavor massless QCD at the renormalization group fixed point from the conformal bootstrap in SU(NF)V symmetric conformal field theories under the assumption that the fixed point is realizable with the lattice regularization based on staggered fermions. We show that the almost identical but slightly stronger bound applies to the regularization based on Wilson fermions (or domain wall fermions) by studying the conformal bootstrap in SU(Nf)L × SU(Nf)R symmetric conformal field theories. For Nf = 8, our bound implies γm< 1.31 to avoid dangerously irrelevant operators that are not compatible with the lattice symmetry.