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 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.

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

Cited by in corpus (9)

• Quantum Field Theory on Noncommutative Spaces
• String Geometry and the Noncommutative Torus
• Duality Symmetries and Noncommutative Geometry of String Spacetime
• Noncommutative Geometry and Spacetime Gauge Symmetries of String Theory
• Target Space Duality in Noncommutative Geometry
• An Effective Superstring Spectral Action
• On deformations of 2d SCFTs
• Strings, Noncommutative Geometry and the Size of the Target Space
• Spectral Geometry of Heterotic Compactifications