(geometry $\leftarrow$ Isbell duality $\to$ algebra)
Regarding the quantized string as a 2-spectral triple, then 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.
Michael Douglas, Two Lectures on D-Geometry and Noncommutative Geometry (arxiv:hep-th/9901146)
Liang Kong, Conformal field theory and a new geometry, in Hisham Sati, Urs Schreiber (eds.) Mathematical Foundations of Quantum Field and Perturbative String Theory (arXiv:1107.3649)
Chien-Hao Liu, Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes (arXiv:1112.4317)
Last revised on April 24, 2017 at 07:50:53. See the history of this page for a list of all contributions to it.