Abstract
The gauged Lorentz theory with torsion has been argued to have an effective theory whose non-trivial background is responsible for background gravitational curvature if torsion is treated as a quantum-mechanical variable against a background of constant curvature. We use the CDG decomposition to argue that such a background can be found without including torsion. Adapting our previously published Clairaut-based treatment of QCD, we go on to study the implications for second quantisation.
Highlights
The dual superconductor model of QCD confinement requires the vacuum to contain a condensate of magnetic monopoles
The apparent existence of destabilising tachyon modes was an issue for some time [2,8,30]. These issues were rectified by the introduction of the CDG decomposition, which specifies the internal direction of the Abelian subgroup in a gauge covariant manner, allowing the internal direction to vary arbitrarily throughout spacetime
The matter was sorted by Bae et al [18], who demonstrated that the DOFs of nwere not canonical but topological, indicating the embedding of the Abelian subgroup in the gauge group
Summary
The dual superconductor model of QCD confinement requires the vacuum to contain a condensate of (chromo) magnetic monopoles This led several authors to consider embedded, usually Abelian, subgroups within gauge groups. There was considerable controversy regarding the stability of such a vacuum These issues were resolved by the Cho–Duan–Ge (CDG) decomposition [4,5], which introduces an internal vector to covariantly allow a subgroup embedding within a theory’s gauge group to vary throughout spacetime. Analyses based on this approach confirmed this magnetic background [1,3] and careful consideration of renormalisation and causality [6–9] resolved such a condensate to be stable through several independent arguments.
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