Supersymmetric quantum mechanics from wrapped branes

TL;DR

This paper constructs explicit solutions in gauged supergravity representing wrapped D6-branes on six-cycles within Calabi-Yau fourfolds, revealing their geometric and topological properties and connecting to M-theory compactifications.

Contribution

It provides explicit supergravity solutions for wrapped D6-branes on six-cycles in Calabi-Yau fourfolds, linking them to M-theory compactifications with SU(5) holonomy.

Findings

Solution preserves two supercharges.

Asymptotically forms a cone with SU(2)^4/U(1)^3 base.

Related higher-dimensional metrics with SU(n+1) holonomy constructed.

Abstract

We explicitly construct a solution of eight-dimensional gauged supergravity representing D6-branes wrapped on six-cycles inside Calabi-Yau fourfolds. The solution preserves two supercharges and asymptotically is a cone with the coset space SU(2)^4/U(1)^3 as its base. It is shown to correspond to an M-theory compactification on a Calabi-Yau manifold with SU(5) holonomy and we discuss in detail its geometrical and topological features. We also construct a family of related higher dimensional metrics having SU(n+1) holonomy, which of course have no brane interpretation.