A review showing that symmetric instantons reduce to hyperbolic monopoles and vortices whose dilute gas yields an area law for the Wilson loop, giving a semi-classical, holographic picture of quark confinement.
Monopoles, instantons and the Helmholtz equation
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abstract
In this work we study the dimensional reduction of smooth circle invariant Yang-Mills instantons defined on 4-manifolds which are non-trivial circle fibrations over hyperbolic 3-space. A suitable choice of the 4-manifold metric within a specific conformal class gives rise to singular and smooth hyperbolic monopoles. A large class of monopoles is obtained if the conformal factor satisfies the Helmholtz equation on hyperbolic 3-space. We describe simple configurations and relate our results to the JNR construction, for which we provide a geometric interpretation.
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Quark confinement consistent with holography due to hyperbolic magnetic monopoles and hyperbolic vortices unifiedly reduced from symmetric instantons
A review showing that symmetric instantons reduce to hyperbolic monopoles and vortices whose dilute gas yields an area law for the Wilson loop, giving a semi-classical, holographic picture of quark confinement.