Instantons: topological aspects

The ADHM Construction and Anselmi's Topological Anomalies

We examine the anomalies arising in instanton calculus as detailed by Damiano Anslemi in 1994. Whereas Anselmi uses BRST theory, we use the ADHM construction to arrive at the same conclusions from a differential-geometric way. We observe that Anselmi's TQFT is similar to Donaldson Theory applied to charge 1 instantons on the 4-sphere,although the latter is really only used for 4-manifolds with non-zero second positive betti number. We demonstrate why the anomalies occur in the case of charge 1 instantons and move to show that similar anomalies cannot occur for instantons of higher charge. To d…

$\mathrm{Spin}(7)$-瞬子的拓扑量子场论

A topological quantum field theory for $\mathrm{Spin}(7)$-instantons

本文基于8维流形上Spin(7)-瞬子模空间构造拓扑量子场论，通过Mathai-Quillen和AKSZ形式主义推导作用量，并证明其可重写为Chern-Simons型理论。