D4-branes wrapped on four-dimensional orbifolds through consistent truncation

We construct a consistent truncation of six-dimensional matter coupled $F(4)$ gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS${}_2\times {\mathrm{\Sigma }}_1$ solutions giving rise to four-dimensional orbifold solutions, AdS${}_2\times {\mathrm{\Sigma }}_1⋉{\mathrm{\Sigma }}_2$. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U$(1{)}^2$-gauged supergravity including all fields and arbitrary Romans mass and gauge coupling. The solutions we construct are naturally interpreted as the near-horizon geometries of asymptotically AdS${}_6$ black holes with a four-dimensional orbifold horizon. Alternatively, one may view them as the holographic duals of superconformal quantum mechanical theories constructed by compactifying five-dimensional USp$(2N)$ theory living on a stack of D4-D8 branes on the four-dimensional orbifolds. As a first step to identifying these quantum mechanical theories we compute the Bekenstein–Hawking entropy holographically.