Obstruction to D-brane topology change

TL;DR

This paper explores how topology change in fuzzy geometry relates to energy and Lie algebra representations in M-theory, proposing a new method to obtain non-commutative solutions that excludes certain topology-changing processes.

Contribution

It introduces a novel approach to derive non-commutative solutions for non-Abelian D-branes, constraining topology change mechanisms in M-theory matrix models.

Findings

Identifies two types of topology change linked to Lie algebra representations.

Proposes a new method to obtain non-commutative solutions in D-brane actions.

Excludes one previously known topology-changing process in M-theory models.

Abstract

A study of the relation between topology change, energy and Lie algebra representations for fuzzy geometry in connection to $M$-theory is presented. We encounter two different types of topology change, related to the different features of the Lie algebra representations appearing in the matrix models of $M$-theory. From these studies, we propose a new method of obtaining non-commutative solutions for the non-Abelian $D$-brane action found by Myers. This mechanism excludes one of the two topology changing processes previously found in other non-commutative solutions of many matrix-based models in $M$-theory i.e. in M(atrix) theory, Matrix string theory and non-Abelian $D$-brane physics.