Bootstrap bound for conformal multi-flavor QCD on lattice

TL;DR

This paper establishes a conformal bootstrap bound on the mass anomalous dimension in multi-flavor QCD, extending previous bounds to Wilson fermion regularizations and providing constraints relevant for lattice simulations.

Contribution

It derives a slightly stronger conformal bootstrap bound on _m for Wilson fermions, applicable to multi-flavor QCD with implications for lattice regularizations.

Findings

Bound _m < 1.31 for N_f=8 to prevent incompatible operators

Extension of bootstrap bounds from staggered to Wilson fermions

Implications for lattice realizability of conformal fixed points

Abstract

The recent work by Iha et al shows an upper bound on mass anomalous dimension $\gamma_m$ of multi-flavor massless QCD at the renormalization group fixed point from the conformal bootstrap in $SU(N_F)_V$ 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 $SU(N_f)_L \times SU(N_f)_R$ symmetric conformal field theories. For $N_f=8$, our bound implies $\gamma_m < 1.31$ to avoid dangerously irrelevant operators that are not compatible with the lattice symmetry.