Abstract
In a recent paper, we developed and applied a dilaton-based effective field theory (EFT) to the analysis of lattice-simulation data for a class of confining gauge theories with near-conformal infrared behavior. It was employed there at the classical level to the SU(3) gauge theory with eight Dirac fermions in the fundamental representation. Here, we explore the structure of the EFT further. We examine its application to lattice data (newly updated) for the SU(3) theory with eight Dirac fermions in the fundamental representation, and the SU(3) theory with two Dirac fermions in the sextet representation. In each case, we determine additional fit parameters and discuss uncertainties associated with extrapolation to zero fermion mass. We highlight universal features, study the EFT at the quantum loop level and discuss the importance of future lattice simulations.
Highlights
In a recent paper, we developed and applied a dilaton-based effective field theory (EFT) to the analysis of lattice-simulation data for a class of confining gauge theories with near-conformal infrared behavior
The relative lightness of the scalar and NGB’s in the lattice simulations suggests that they be treated via an effective field theory (EFT) with only these degrees of freedom
We extend our treatment of this EFT, exploring its features at both the classical and quantum levels and extending the comparison with lattice data to include Nf = 2 Dirac fermions in the 2-index symmetric representation [6,7,8]
Summary
To describe the light states appearing in lattice simulations, we employ an EFT consisting of the NGB’s along with a description of a light singlet scalar consistent with its interpretation as a dilaton. Where the Σ field describes the NGB’s arising from the spontaneous breaking of chiral symmetry It transforms as Σ → ULΣUR† , with UL and UR the matrices of SU(Nf )L and SU(Nf )R transformations, and satisfies the nonlinear constraint ΣΣ† = I. The form of LM is such that it breaks scale and chiral symmetries in the same way as the fermion-bilinear mass term in the underlying gauge theory [15], with y taken to be the scaling dimension of ψψ. This is an RG-scale dependent quantity; in the present context it should be taken to be defined at scales above the confinement scale, where the gauge coupling varies slowly. We allow the lattice data to determine certain features of the potential
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