Geometry from Matrices via D-branes

TL;DR

This paper develops a method to derive commutative geometries from matrix configurations representing D-brane bound states, connecting matrix models with geometric descriptions in string theory.

Contribution

It introduces a new map from matrices to geometry using D-brane tachyons, aligning with recent proposals and providing a matrix regularization of geometry.

Findings

The matrix-to-geometry map matches recent proposals.

The map acts as a matrix regularization in the large N limit.

Tachyons in unstable D-brane systems are crucial for the map's construction.

Abstract

In this paper, we give a map from matrices to a commutative geometry from a bound state of a D2-brane and N D0-branes. For this, tachyons in auxiliary unstable D-brane system describing the bound state play crucial roles. We found the map obtained in this way coincides with the recent proposals. We also consider the map from the geometry to matrices in a large N limit and argue that the map is a matrix regularization of geometry.