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

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

2005-10-17

arxiv.org/abs/hep-th/0510144v2

JHEP0601:030,2006

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, Latex; v2: Minor correction in conformal transformation of couplings, references added

Scientific paper

10.1088/1126-6708/2006/01/030

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.

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