Target Space Duality in Noncommutative Geometry

TL;DR

This paper explores how spacetime duality and worldsheet symmetries in string theory can be understood within noncommutative geometry, using spectral triples and vertex operator algebras to model dualities as automorphisms.

Contribution

It introduces a framework where spacetime duality in string theory is represented through noncommutative geometry, linking dualities to automorphisms of vertex operator algebras.

Findings

Duality group identified as a subgroup of automorphisms of vertex operator algebra

Spacetime duality linked to independent Dirac operators from worldsheet chirality

Noncommutative geometry provides a natural setting for string dualities

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.