Why do instantons exist in lattice gauge theory?



According to Polyakov, the 2+1 dimensional compact U(1) lattice gauge
theory is in the confining phase, due to the disturbance of the
instantons. The instantons are point like topological defects in the
2+1 dimension.

However, the second homotopy group of the U(1) group space is trivial,
which should exclude point like topological defects in the 2+1
dimension.

Why do Polyakov's instantons exist in 2+1D U(1) lattice gauge theory?

-Max

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