Supersymmetric quantum mechanics from wrapped D4-branes

We find a large class of holographic solutions describing D4-branes wrapped on 4-manifolds ${\mathcal{M}}_4$ with constant curvature leading to gravity duals of supersymmetric quantum mechanics in the IR via twisted compactifications. The manifolds ${\mathcal{M}}_4$ considered here are four-dimensional spheres and hyperbolic spaces, products of two Riemann surfaces, and Kahler four-cycles. The solutions are obtained from the maximal gauged supergravity in six dimensions with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)⋉{\mathbb{R}}^4$ gauge groups. These gauged supergravities can be embedded in type IIA theory via consistent truncations on $H^{p,q}\times {\mathbb{R}}^{5-p-q}$ and $H^{p,q}\times {\mathbb{R}}^{4-p-q}\times S^1$, respectively. The solutions take the form of $t\times {\mathcal{M}}_4$-sliced domain walls interpolating between locally flat domain walls and singular geometries in the IR. Upon uplifted to type IIA theory, many solutions admit physical IR singularities and could holographically describe supersymmetric quantum mechanics arising from twisted compactifications of D4-branes on ${\mathcal{M}}_4$.