 97413 F. Lizzi, R.J. Szabo
 Duality Symmetries and Noncommutative Geometry of String Spacetime.
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Jul 24, 97

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Abstract. We examine the structure of spacetime symmetries of toroidally
compactified
string theory within the framework of noncommutative geometry. Following
a proposal of Frohlich and Gawedzki, we describe the noncommutative string
spacetime using a detailed algebraic construction of the vertex operator
algebra. We show that the spacetime duality and discrete worldsheet
symmetries of the string theory are a consequence of the existence of two
independent Dirac operators, arising from the chiral structure of the
conformal field theory. We show that these operators are also responsible
for the emergence of ordinary classical spacetime as a lowenergy limit of
the string spacetime, and from this we establish a relationship between
Tduality and changes of spin structure of the target space manifold. We
study the automorphism group of the vertex operator algebra and show that
spacetime duality is naturally a gauge symmetry in this formalism. We show
that classical general covariance also becomes a gauge symmetry of the
string spacetime. We explore some larger symmetries of the algebra in the
context of a universal gauge group for string theory, and connect these
symmetry groups with some algebraic structures which arise in the
theory of vertex operator algebras, such as the Monster group. We also
briefly describe how the classical topology of spacetime is modified by
the string theory, and calculate the cohomology groups of the
noncommutative spacetime. A selfcontained, pedagogical introduction to
the techniques of noncommutative geometry is also included.
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