Perfect topological charge for asymptotically free theories
Abstract
The classical equations of motion of the perfect lattice action in asymptotically free d=2 spin and d=4 gauge models possess scale invariant instanton solutions. This property allows the definition of a topological charge on the lattice which is perfect in the sense that no topological defects exist. The basic construction is illustrated in the d=2 O(3) non--linear σ--model and the topological susceptibility is measured to high precision in the range of correlation lengths ∈ (2 - 60). Our results strongly suggest that the topological susceptibility is not a physical quantity in this model.
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