Topology and higher dimensional representations

Abstract

SU(3) gauge theory in the 2-index symmetric (sextet) and fundamental representations is considered in symmetric and periodic boxes. Using the overlap formulation in the quenched approximation it is shown that the topological charge obtained from the sextet index theorem always leads to an integer value and agrees with the charge obtained from the fundamental index theorem in the continuum. At larger lattice spacing configurations exist with fractional topological charge if the sextet index is used but these are lattice artifacts and the probability of finding such a configuration rapidly approaches zero. By considering the decomposition of the sextet representation with respect to an SU(2) subgroup it is shown that the SU(2) adjoint index theorem leads to integer charge as well. We conclude that the non-zero value of the bilinear gaugino condensate in N=1 super-Yang-Mills theory cannot be attributed to configurations with fractional topological charge once periodic boundary conditions are imposed.

14 pages, 7 figures; discussion and references added

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Cited by in corpus (21)

• Nearly conformal gauge theories in finite volume
• Hyperscaling relations in mass-deformed conformal gauge theories
• Mass anomalous dimension in SU(2) with two adjoint fermions
• Mesonic spectroscopy of Minimal Walking Technicolor
• Finite-size scaling tests for SU(3) lattice gauge theory with color sextet fermions
• Deconfinement Phase Transition in Compact Stars : Maxwell vs. Gibbs Construction of the Mixed Phase
• Conformal Window of Gauge Theories with Four-Fermion Interactions and Ideal Walking
• Mass anomalous dimension in SU(2) with six fundamental fermions
• Chiral properties of SU(3) sextet fermions
• The S Parameter in QCD from Domain Wall Fermions
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Higher Representations Duals
• Flavor Dependence of the S-parameter
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• Deconfinement in Yang-Mills theory through toroidal compactification with deformation
• A linear sigma model for multiflavor gauge theories
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Technicolor and Beyond: Unification in Theory Space
• Extreme Technicolor & The Walking Critical Temperature
• Monte-Carlo simulations of overlap Majorana fermions
• Comparison of smoothening flows for the topological charge in QCD-like theories