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Minimal Walking on the Lattice

Simon Catterall, Francesco Sannino

TL;DR

The paper investigates walking dynamics in a four-dimensional SU(2) gauge theory with two Dirac fermions in the two-index symmetric representation, proposing it as a minimal walking theory near an infrared fixed point. Using lattice simulations, the authors compare symmetric-representation fermions to fundamental ones on identical volumes, finding substantially lighter hadron masses and a non-monotonic dependence on the gauge coupling $\beta$ for the symmetric case, consistent with walking. The results suggest a light scale $\Lambda_{\rm latt}$ and potential approach to a conformal phase at large $\beta$, though finite-volume effects limit definitive conclusions. These findings support the viability of minimal walking technicolor scenarios and motivate larger-scale lattice studies to measure running couplings directly and to test for true infrared conformality.

Abstract

We provide the first evidence of a walking dynamics for two color lattice Yang-Mills theory with two Dirac flavors in the symmetric representation of the gauge group.

Minimal Walking on the Lattice

TL;DR

The paper investigates walking dynamics in a four-dimensional SU(2) gauge theory with two Dirac fermions in the two-index symmetric representation, proposing it as a minimal walking theory near an infrared fixed point. Using lattice simulations, the authors compare symmetric-representation fermions to fundamental ones on identical volumes, finding substantially lighter hadron masses and a non-monotonic dependence on the gauge coupling for the symmetric case, consistent with walking. The results suggest a light scale and potential approach to a conformal phase at large , though finite-volume effects limit definitive conclusions. These findings support the viability of minimal walking technicolor scenarios and motivate larger-scale lattice studies to measure running couplings directly and to test for true infrared conformality.

Abstract

We provide the first evidence of a walking dynamics for two color lattice Yang-Mills theory with two Dirac flavors in the symmetric representation of the gauge group.

Paper Structure

This paper contains 10 sections, 8 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Review of some Theoretical and Phenomenological aspects of Higher Dimensional Representations
  3. Conformal Window
  4. Minimal Walking Technicolor
  5. Lattice Theory
  6. Numerical Results
  7. Pion and rho mass
  8. Pion decay constant
  9. Scaling
  10. Summary

Figures (12)

  • Figure 1: Phase diagram for theories with fermions in the: i) fundamental representation (grey), ii) two-index antisymmetric (blue), iii) two-index symmetric (red), iv) adjoint representation (green) as a function of the number of flavors and the number of colors. The shaded areas depict the corresponding conformal windows. The upper solid curve represents the loss of asymptotic freedom, the lower curve loss of chiral symmetry breaking. The dashed curves show the existence of a Banks--Zaks fixed point. Picture taken from Dietrich:2006cm.
  • Figure 2: Top Left Panel: QCD-like behavior of the coupling constant as function of the momentum (Running). Top Right Panel: Walking-like behavior of the coupling constant as function of the momentum (Walking). Bottom Right Panel: Cartoon of the beta function associated to a generic walking theory.
  • Figure 3: Pion mass squared vs quark mass for fundamental quarks
  • Figure 4: Pion mass squared vs quark mass for symmetric quarks
  • Figure 5: Rho mass vs quark mass for fundamental quarks
  • ...and 7 more figures