Supersymmetric quantum mechanics from wrapped D4-branes

TL;DR

This paper constructs a broad class of holographic solutions from wrapped D4-branes on 4-manifolds, providing gravity duals of supersymmetric quantum mechanics via twisted compactifications, using six-dimensional gauged supergravity embedded in type IIA string theory.

Contribution

It introduces new holographic solutions for D4-branes wrapped on various 4-manifolds, derived from maximal gauged supergravity and embedded in type IIA theory, expanding the understanding of supersymmetric quantum mechanics holography.

Findings

Solutions describe D4-branes on spheres, hyperbolic spaces, and Kahler cycles.

Many solutions exhibit IR singularities suitable for holographic duals.

The solutions interpolate between flat and singular geometries in the IR.

Abstract

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 $CSO(p,q,4-p-q)\ltimes \mathbb{R}^4$ 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 $\mathcal{M}_4$.