Strings, Noncommutative Geometry and the Size of the Target Space

Details Strings, Noncommutative Geometry and the Size of the Target Space Strings, Noncommutative Geometry and the Size of the Target Space

1999-02-25

arxiv.org/abs/hep-th/9902187v1

Int.J.Mod.Phys. A14 (1999) 4501-4518

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LateX, instructions for older LateX versions

Scientific paper

10.1142/S0217751X99002116

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge non invariant quantity. This generalizes the R <--> 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,Z). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

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