Noncommutative geometry, Quantum effects and DBI-scaling in the collapse of D0-D2 bound states

TL;DR

This paper investigates the fluctuations of fuzzy two-sphere solutions in the non-abelian DBI action of D0-branes, revealing a duality with D2-brane descriptions, and explores a large-N scaling limit where non-linearities persist.

Contribution

It introduces a large-N DBI-scaling limit that retains non-linear effects and analyzes the quantum and classical behavior of D0-D2 bound states within this framework.

Findings

Quadratic fluctuations match dual D2-brane descriptions.

Solvable Lamé equations describe some fluctuation modes.

Identifies a critical radius with strong gauge coupling effects.

Abstract

We study fluctuations of time-dependent fuzzy two-sphere solutions of the non-abelian DBI action of D0-branes, describing a bound state of a spherical D2-brane with N D0-branes. The quadratic action for small fluctuations is shown to be identical to that obtained from the dual abelian D2-brane DBI action, using the non-commutative geometry of the fuzzy two-sphere. For some of the fields, the linearized equations take the form of solvable Lam\'e equations. We define a large-N DBI-scaling limit, with vanishing string coupling and string length, and where the gauge theory coupling remains finite. In this limit, the non-linearities of the DBI action survive in both the classical and the quantum context, while massive open string modes and closed strings decouple. We describe a critical radius where strong gauge coupling effects become important. The size of the bound quantum ground state of multiple D0-branes makes an intriguing appearance as the radius of the fuzzy sphere, where the maximal angular momentum quanta become strongly coupled.