The Spectral Action Principle in Noncommutative Geometry and the Superstring
High Energy Physics - Theory
2009-10-30 v3
Abstract
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 action principle is then used to determine a spectral action valid for the fluctuations of the string modes.
Cite
@article{arxiv.hep-th/9701096,
title = {The Spectral Action Principle in Noncommutative Geometry and the Superstring},
author = {A. H. Chamseddine},
journal= {arXiv preprint arXiv:hep-th/9701096},
year = {2009}
}
Comments
Latex file, 13 pages. Correction to equation 47, which should read Tr| |^2 and not |Tr |^2. Final form to appear in Physics Letters B