Dilaton Effective Field Theory across the Conformal Edge

TL;DR

Dilaton effective field theory (dEFT) serves as a diagnostic tool to distinguish near-conformal confining theories from infrared conformal ones using lattice data, with applications demonstrated on specific gauge theories.

Contribution

This work shows how dEFT can be used to analyze lattice data to differentiate between confining and conformal gauge theories near the conformal edge.

Findings

Analysis favors confinement in SU(3) with 8 flavors.

Analysis favors conformality in SU(2) with 1 adjoint fermion.

Framework can be refined with future lattice measurements.

Abstract

Dilaton effective field theory (dEFT) can be employed to analyze lattice data in gauge theories that lie in close proximity of the lower edge of the conformal window. Under special conditions, we show that it can be used as a diagnostic tool to distinguish near-conformal, yet confining, theories from infrared conformal ones. We demonstrate this efficacy by analyzing two sets of lattice measurements taken from the literature. For the $SU(3)$ theory coupled to $N_f=8$ Dirac fermions transforming in the fundamental representation, our analysis favors confinement. For the $SU(2)$ theory with $N_f=1$ adjoint fermion, our fits favor infrared conformal behavior. We discuss future lattice measurements, and analysis refinements, that can further test this framework.