Equivariant localization for wrapped M5-branes and D4-branes

Following the work of [1], we consider six- and seven-dimensional gauged supergravity coupled to a vector multiplet on an ansatz of $AdS_{4,5}\times{M}_2$, respectively, where $M_2$ is a two-dimensional surface with a Killing vector. We construct equivariantly closed forms from spinor bilinears of K