Instantons and Monopoles in General Abelian Gauges
Oliver Jahn (U Erlangen)
TL;DR
This paper establishes a mathematical relation linking instanton numbers to magnetic monopoles in SU(2) Yang-Mills theory, revealing how monopole twists contribute to instanton topological charge.
Contribution
It introduces a novel expression of the instanton number as a sum of monopole twists, connecting topological invariants with monopole quantum numbers in general Abelian gauges.
Findings
Instanton number equals the sum of monopole twists.
Monopole twists are related to a generalized Hopf invariant.
Stronger instanton-monopole relations in the Polyakov gauge.
Abstract
A relation between the total instanton number and the quantum-numbers of magnetic monopoles that arise in general Abelian gauges in SU(2) Yang-Mills theory is established. The instanton number is expressed as the sum of the `twists' of all monopoles, where the twist is related to a generalized Hopf invariant. The origin of a stronger relation between instantons and monopoles in the Polyakov gauge is discussed.
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