  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.
