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

TL;DR

This paper develops a method to construct and uplift solutions describing near-horizon geometries of AdS$_6$ black holes with orbifold horizons, linking supergravity solutions to dual quantum mechanical theories.

Contribution

It introduces a consistent truncation of six-dimensional supergravity on various surfaces and provides explicit uplift formulas to massive type IIA supergravity, connecting black hole solutions to dual quantum theories.

Findings

Constructed new orbifold solutions in supergravity.

Uplifted solutions to massive type IIA supergravity.

Computed holographic entropy for dual quantum theories.

Abstract

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$_2\times {\Sigma}_1$ solutions giving rise to four-dimensional orbifold solutions, AdS$_2\times{\Sigma}_1\ltimes{\Sigma}_2$. 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.