Casimir Scaling and String Breaking in G(2) Gluodynamics

Abstract

We study the potential energy between static charges in G(2) gluodynamics in three and four dimensions. Our work is based on an efficient local hybrid Monte-Carlo algorithm and a multi-level Lüscher-Weisz algorithm with exponential error reduction to accurately measure expectation values of Wilson- and Polyakov loops. Both in three and four dimensions we show that at intermediate scales the string tensions for charges in various G(2)-representations scale with the second order Casimir. In three dimensions Casimir scaling is confirmed within one percent for charges in representations of dimensions 7, 14, 27, 64, 77, 77', 182 and 189 and in 4 dimensions within 5 percent for charges in representions of dimensions 7, 14, 27 and 64. In three dimensions we detect string breaking for charges in the two fundamental representations. The scale for string breaking agrees very well with the mass of the created pair of glue-lumps.

20 pages, 17 figures

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• The phase diagram of a gauge theory with fermionic baryons
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• Phase diagram of the lattice G(2) Higgs Model
• On the gauge-algebra dependence of Landau-gauge Yang-Mills propagators
• Glueballs and the Yang-Mills plasma in a $T$-matrix approach
• Topological aspects of G2 Yang-Mills theory
• A study of the influence of the gauge group on the Dyson-Schwinger equations for scalar-Yang-Mills systems
• Flux tubes and string breaking in three dimensional SU(2) Yang-Mills theory
• The structure of the Yang-Mills spectrum for arbitrary simple gauge algebras
• Mass spectrum of $2$-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory on the lattice
• Constructing a neutron star in G2-QCD
• Quark Confinement in Restricted SU(2) Gauge Theory
• Confinement in G(2) Gauge Theories Using Thick Center Vortex Model and domain structures
• G2 monopoles
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis I. The effective action from chiral scalars
• Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
• Cho decomposition, Abelian gauge fixing and monopoles in G(2) Yang-Mills theory
• Color screening in flux tubes and in the color Coulomb potential from the QCD Field Correlators
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis II. The measure for gauge fields and a 4d WZW theory
• $F_4$ , $E_6$ and $G_2$ Exceptional Gauge Groups in Vacuum Domain Structure Model
• Confinement, Casimir scaling and phase transitions in G(2) gauge theories
• Remarks on the Confinement in the $G(2)$ Gauge Theory Using the Thick Center Vortex Model
• The Structure Constants of the Exceptional Lie Algebra ${\mathfrak{g}}_2$ in the Cartan-Weyl Basis
• Lattice simulations of $G_2$-QCD at finite density