Open superstring and noncommutative geometry

Open Superstring and Noncommutative Geometry

We perform canonical quantization of the open Neveu-Schwarz-Ramond (NSR) superstrings in the background of a D-brane with the NS B-field. If we choose the mixed boundary condition as a primary constraint, it generates a set of secondary constraints. These constraints are easily solved and as a result, the noncommutative geometry in the bosonic string theory is extended to the superspace. Solvin...

Lattice superstring and noncommutative geometry

Recent developments in superstring theory and noncommutative geometry are deeply related to the idea of Eguchi-Kawai reduction in large N gauge theories which dates back to early 80s. After a general review on this subject including revived interests in solving planar QCD, we present some results in the superstring matrix model suggesting the dynamical generation of 4d space-time due to the col...

The Spectral Action Principle in Noncommutative Geometry and the Superstring

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all tools of noncommutative geometry. In particular, we apply this to the N = 1 supersymmetric non-linear sigma model and derive an expression for the generalized loop space Dirac operator, in presence of a general background, using canonical quantization. The spectral actio...

Canonical Quantization of Open String and Noncommutative Geometry

We perform canonical quantization of open strings in the D-brane background with a B-field. Treating the mixed boundary condition as a primary constraint, we get a set of secondary constraints. Then these constraints are shown to be equivalent to orbifold conditions to be imposed on normal string modes. These orbifold conditions are a generalization of the familiar orbifold conditions which ari...

Noncommutative geometry