Noncommutative Manifolds from the Higgs Sector of Coincident D-Branes

TL;DR

This paper explores how the Higgs sector of coincident D-branes can be used to construct noncommutative manifolds, linking string theory and noncommutative geometry.

Contribution

It introduces a method to derive noncommutative manifolds from the Higgs sector of coincident D-branes, extending the understanding of noncommutative geometry in string theory.

Findings

Coordinates and momenta take values in Lie algebras

Construction of noncommutative C*-algebras from manifolds

Framework for noncommutative geometry from D-branes

Abstract

The Higgs sector of the low-energy physics of n of coincident D-branes contains the necessary elements for constructing noncommutative manifolds. The coordinates orthogonal to the coincident branes, as well as their conjugate momenta, take values in the Lie algebra of the gauge group living inside the brane stack. In the limit when n=\infty (and in the absence of orientifolds), this is the unitary Lie algebra u(\infty). Placing a smooth manifold K orthogonally to the stack of coincident D-branes one can construct a noncommutative C*-algebra that provides a natural definition of a noncommutative partner for the manifold K.