nLab D-brane geometry



String theory

Noncommutative geometry



Regarding the quantum string as a 2-spectral triple, it defines a spectral geometry (typically but not necessarily a noncommutative geometry) which is the effective spacetime as seen by this quantum string (as read of from, notably, its energy spectrum). For the open string the most prominent aspect of its 2d SCFT worldsheet theory are its boundary conditions. In the spectral interpretation these correspond to the presence of D-branes in the effective target spacetime. Much geometric information is contained in these D-brane states, and the resulting concept of (noncommutative) geometry has accordingly been called D-brane geometry or D-geometry for short.


Fuzzy spheres

The fuzzy spheres appear in D-brane geometry:

  1. the fuzzy funnels of Dp-D(p+2)-brane intersections have fuzzy 2-sphere slices

  2. the fuzzy funnels of Dp-D(p+4)-brane intersections have fuzzy 4-sphere slides

  3. the supersymmetric classical solutions of the BMN matrix model are precisely fuzzy 2-sphere configurations (BMN 02 (5.4)).


With emphasis on the IKKT matrix model and the noncommutative geometry of fuzzy spheres:

Last revised on March 14, 2020 at 07:20:30. See the history of this page for a list of all contributions to it.