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Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions

Yigal Shamir, Benjamin Svetitsky, Thomas DeGrand

TL;DR

This study uses the Schrödinger functional to nonperturbatively map the discrete beta function for SU(3) gauge theory with two sextet fermions, finding a zero near $g^2\approx 2.0$ that suggests an infrared-attractive fixed point, in tension with perturbative expectations that place the fixed point at much stronger coupling ($g^{*2}\approx10.4$). By analyzing the massless theory on multiple lattice spacings and examining confinement and chiral-symmetry signals, the authors argue that the zero cannot be attributed to confinement or chiral-symmetry breaking in the explored volumes, pointing toward conformal dynamics in the IR. The work highlights the potential for rich IR behavior in higher-representation fermion systems and motivates further scaling studies and mass-deformation analyses to clarify the RG flow and its continuum limit. If confirmed, the results would place the massless two-sextet theory in the conformal window and challenge walking-like scenarios for beyond-Standard-Model model building.

Abstract

We have carried out a Schrodinger functional (SF) calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the SF renormalized coupling is in the neighborhood of g^2=2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.

Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions

TL;DR

This study uses the Schrödinger functional to nonperturbatively map the discrete beta function for SU(3) gauge theory with two sextet fermions, finding a zero near that suggests an infrared-attractive fixed point, in tension with perturbative expectations that place the fixed point at much stronger coupling (). By analyzing the massless theory on multiple lattice spacings and examining confinement and chiral-symmetry signals, the authors argue that the zero cannot be attributed to confinement or chiral-symmetry breaking in the explored volumes, pointing toward conformal dynamics in the IR. The work highlights the potential for rich IR behavior in higher-representation fermion systems and motivates further scaling studies and mass-deformation analyses to clarify the RG flow and its continuum limit. If confirmed, the results would place the massless two-sextet theory in the conformal window and challenge walking-like scenarios for beyond-Standard-Model model building.

Abstract

We have carried out a Schrodinger functional (SF) calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the SF renormalized coupling is in the neighborhood of g^2=2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.

Paper Structure

This paper contains 6 sections, 8 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Schrodinger functional method
  3. Lattice calculation of the discrete beta function
  4. Nonconfinement and chiral symmetry
  5. Nonconfinement and chiral symmetry
  6. DISCUSSION

Figures (2)

  • Figure 1: Discrete beta function for the scale transformation $L\to2L$, as defined in Eq. (\ref{['Beta']}). The lattice spacing is fixed such that $L=4a$. The dashed curve is the two-loop result. The data points are calculated at bare couplings (left to right) $\beta=5.2$ to 6.0 by 0.1, and then $\beta=7.0$ and 8.0. Horizontal error bars are the size of the plotted symbols.
  • Figure 2: Discrete beta function for the scale transformation $L\to4L/3$. The lattice spacing is fixed such that $L=6a$. The dashed curve is the two-loop result. The data points are calculated at the same bare couplings as in Fig. \ref{['fig:Beta']}. Horizontal error bars are the size of the plotted symbols.