Dilaton Effective Field Theory across the Conformal Edge

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.

💡 Research Summary

The authors develop and apply a dilaton effective field theory (dEFT) framework to distinguish between near‑conformal but confining gauge theories and truly infrared‑conformal ones that sit just inside the conformal window. The dEFT Lagrangian contains a canonically normalized dilaton field χ with a potential V(χ)=Aχ⁴+Bχ^Δ and a set of pseudo‑Nambu‑Goldstone bosons (pNGBs) described by a matrix Σ. The potential parameters A, B, Δ, the scaling exponent y of the explicit fermion‑mass term, and the overall normalization P are treated as fit parameters to be determined from lattice data.

From the potential, the vacuum expectation value F_d of χ is obtained by extremizing the full scalar potential W(χ)=V(χ)−½xN_fRχ^y, where R∝m is proportional to the underlying fermion mass. The dilaton mass M_d, the pNGB decay constant F_π, and the pNGB mass M_π are expressed in terms of F_d, A, B, Δ, y, and P. By eliminating the explicit dependence on the unknown potential shape, three independent fit equations are derived: (9) M_π²F_π^{2−y}=C m, (10) a relation that removes the exponential y‑dependence, and (11) a similar relation for the dilaton mass. These equations allow a simultaneous fit of all lattice observables (F_π², M_π², M_d²) across several fermion‑mass points.

The first case studied is SU(3) gauge theory with N_f=8 Dirac fermions in the fundamental representation. Using five mass points (15 data entries) from Refs.