The spectral action principle in noncommutative geometry and the superstring
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 nonlinear 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.
 Publication:

Physics Letters B
 Pub Date:
 February 1997
 DOI:
 10.1016/S03702693(97)003341
 arXiv:
 arXiv:hepth/9701096
 Bibcode:
 1997PhLB..400...87C
 Keywords:

 High Energy Physics  Theory
 EPrint:
 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