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| D0-brane | |
|---|---|
| Name | D0-brane |
| Type | D-brane |
| Theory | String theory |
D0-brane is a pointlike nonperturbative object in type IIA string theory described as a Dirichlet-brane with zero spatial extent. It appears in the spectrum of Polchinski's formulation of Dirichlet objects and played a central role in proposals linking Witten's M-theory to matrix models. Its properties connect to many developments associated with Maldacena, Banks, Seiberg, Douglas, Susskind, and Strominger.
A D0-brane is defined by imposing Dirichlet boundary conditions on open strings in all nine spatial directions of Type IIA, leaving time as a Neumann direction, and therefore is charged under the Ramond-Ramond one-form potential studied by Townsend and Johnson. The tension and mass of the D0-brane are determined by the string coupling and string length scale used in works by Polchinski and appear in semiclassical analyses by Schwarz and John Schwarz. Charge quantization relates to K-theory classifications developed by Witten and Segal. The D0-brane supports open string end states connecting to other D-branes as explored by Polchinski, Green, Schwarz again and studied in perturbative analyses by Johnson.
The worldvolume of a D0-brane carries a supersymmetric quantum mechanics described in early studies by Douglas and Yin that preserves sixteen supercharges related to Type IIA supergravity invariances discussed by Bergshoeff and Paul Townsend. Low-energy dynamics are encoded in a dimensional reduction of ten-dimensional Super Yang–Mills explored by Witten, Seiberg, and Banks. Fermionic zero modes reflect spacetime supersymmetry patterns analyzed in papers by Seiberg and Witten; central charges and BPS conditions connect to classic results of Strominger and Vafa.
D0-branes provide a nonperturbative probe of M-theory via their interpretation as Kaluza–Klein modes along the compactified eleventh dimension argued by Banks and Witten. They serve in duality maps between Type IIA and compactified M-theory as in analyses by Witten, Maldacena, and Hull. D0-branes are central to understanding U-duality multiplets studied by Sen and Green, and their spectrum interacts with black hole microstate counting pioneered by Strominger and Vafa.
Interactions of D0-branes occur through open string exchanges and closed string emission computed in seminal calculations by Polchinski and Douglas. Scattering amplitudes and effective potentials between D0-branes were derived in one-loop matrix model computations by Banks, Fischler, and Susskind. Gravitational backreaction and supergravity solutions for collections of D0-branes were constructed by Horowitz and Strominger and linked to extremal black hole geometries investigated by Gibbons and Hawking. Nonabelian interactions when multiple D0-branes coincide are described by U(N) quantum mechanics introduced by Douglas and Moore.
The BFSS conjecture proposing a matrix model formulation of M-theory identifies D0-brane quantum mechanics as fundamental, a proposal by Banks, Fischler, Shenker, and Susskind. Matrix theory uses large N limits analyzed by Seiberg and Polchinski to reproduce supergravity interactions discussed by Gopakumar and Verlinde. Evidence involving graviton scattering, bound state spectra, and DLCQ constructions was provided in works by Strominger, Vafa, and Eric Verlinde.
Bound states of D0-branes appear as threshold bound states studied by Witten, Douglas, and analyses of Kaluza–Klein modes by Townsend. On toroidal compactifications the behavior of D0-branes intertwines with T-duality studied by Sen and Hull and gives rise to wrapped D-brane configurations analyzed by Maldacena and Vafa. Nonperturbative bound state counting and index computations connect to instanton calculus developed by Nekrasov and Pestun and to microstate counting of black holes by Strominger and Vafa.
D0-branes are instrumental in tests of AdS/CFT through matrix model limits invoked by Maldacena, and appear in dual descriptions relating Type IIA on compact spaces to M-theory on circles as emphasized by Witten and Hull. They contribute to understanding nonperturbative string dynamics used by Douglas, Seiberg, and Polchinski in studies of S-duality and T-duality. Applications span black hole entropy, matrix cosmology pursued by Banks and Susskind, and refined indices in supersymmetric gauge theories in work by Nekrasov and Pestun.