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How does homotopy apply to instantons with fermionic zero modes?

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When we add fermions to Yang-Mills, fermionic zero modes are required to have a non-vanishing amplitude, a la the Atiyah-Singer index theorem. If we consider a scattering amplitude where fermions come in (out) to (from) infinity, then the gauge fields do not vanish on S⁴, so how do we use homotopy to classify the possible instantons?

related to an answer for: Why are the Yang-Mills instantons classified by the 3rd homotopy group of $S^3$?

asked Aug 29, 2023 in Theoretical Physics by anonymous [ no revision ]

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