D-brane Actions on Kahler Manifolds

TL;DR

This paper investigates the conditions for D-brane actions on Kahler manifolds, showing that Ricci flatness is necessary for their axioms to hold, which may imply Ricci flatness in Matrix theory.

Contribution

It demonstrates that D-brane actions satisfying D-geometry axioms require Ricci flat metrics, providing a potential argument for Ricci flatness in Matrix theory.

Findings

Axioms are only satisfied if the metric is Ricci flat

Ricci flat D-brane actions can be constructed

Potential link between Ricci flatness and Matrix theory

Abstract

We consider actions for N D-branes at points in a general Kahler manifold, which satisfy the axioms of D-geometry, and could be used as starting points for defining Matrix theory in curved space. We show that the axioms cannot be satisfied unless the metric is Ricci flat, and argue that such actions do exist when the metric is Ricci flat. This may provide an argument for Ricci flatness in Matrix theory.