Target Space Duality in Noncommutative Geometry

Abstract

The structure of spacetime duality and discrete worldsheet symmetries of compactified string theory is examined within the framework of noncommutative geometry. The full noncommutative string spacetime is constructed using the Frohlich-Gawedzki spectral triple which incorporates the vertex operator algebra of the string theory. The duality group appears naturally as a subgroup of the automorphism group of the vertex operator algebra and spacetime duality is shown to arise as the possibility of associating two independent Dirac operators, arising from the chiral structure of the worldsheet theory, to the noncommutative geometry.

8 pages Latex

References in corpus (3)

• An Introduction to Noncommutative Spaces and their Geometry
• Noncommutative Geometry and D-Branes
• The Spectral Action Principle in Noncommutative Geometry and the Superstring

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• Internal Space for the Noncommutative Geometry Standard Model and Strings
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• Euclidean Pseudoduality and Boundary Conditions in Sigma Models
• The Structure of Spacetime and Noncommutative Geometry
• Spectral Geometry of Heterotic Compactifications
• T-duality for open strings in the presence of backgrounds and noncommutativity