Ricci-Flat Branes

TL;DR

This paper generalizes D8-brane solutions in massive type IIA supergravity by allowing the worldvolume to be any Ricci-flat manifold with Killing spinors, leading to new supersymmetric configurations with gravitational instantons.

Contribution

It introduces a framework for constructing supersymmetric brane solutions with Ricci-flat worldvolumes admitting Killing spinors, extending previous models.

Findings

Supersymmetric solutions with Ricci-flat worldvolumes are possible.

Existence of Killing spinors relates to self-duality of curvature.

Worldvolume can be gravitational instantons.

Abstract

Up to overall harmonic factors, the D8-brane solution of the massive type IIA supergravity theory is the product of nine-dimensional Minkowski space (the worldvolume) with the real line (the transverse space). We show that the equations of motion allow for the worldvolume metric to be generalised to an arbitrary Ricci-flat one. If this nine-dimensional Ricci-flat manifold admits Killing spinors, then the resulting solutions are supersymmetric and satisfy the usual Bogomol'nyi bound, although they preserve fewer than the usual one half of the supersymmetries. We describe the possible choices of such manifolds, elaborating on the connection between the existence of Killing spinors and the self-duality condition on the curvature two-form. Since the D8-brane is a domain wall in ten dimensions, we are led to consider the general case: domain walls in any supergravity theory. Similar considerations hold here also. Moreover, it is shown that the worldvolume of any magnetic brane --- of which the domain walls are a specific example --- can be generalised in precisely the same way. The general class of supersymmetric solutions have gravitational instantons as their spatial sections. Some mention is made of the worldvolume solitons of such branes.