Non-commutativity, Zero modes and D-brane Geometry

TL;DR

This paper explores the non-commutative geometry of D p-branes through open string theory, revealing how non-commutativity arises from a re-normalized world-volume and connecting it to zero modes and holography.

Contribution

It provides a new perspective on non-commutative geometry in D p-branes by analyzing world-sheet correlators and gauge symmetries, linking large B-field limits to holographic principles.

Findings

Non-commutativity corresponds to a re-normalized world-volume.

U(1) gauge symmetry maps to a homomorphic image in non-commutative space.

Large B-field limit reduces non-commutativity to zero modes, aligning with holography.

Abstract

The non-commutative geometry is revisited from the perspective of a generalized D p-brane. In particular, we analyze the open bosonic string world-sheet description and show that an effective non-commutative description on a D p-brane corresponds to a re-normalized world-volume. The world-volume correlators are analyzed to make a note on the non-commutative geometry. It is argued that the U(1) gauge symmetry can be viewed in a homomorphic image space for the non-commutative space of coordinates with an SO(p) symmetry. In the large B-field limit, the non-commutativity reduces to that among the zero modes and the world-volume description is precisely in agreement with the holographic principle.