# String Geometry and the Noncommutative Torus

@article{Landi1999StringGA, title={String Geometry and the Noncommutative Torus}, author={Giovanni Landi and Fedele Lizzi and Richard Joseph Szabo}, journal={Communications in Mathematical Physics}, year={1999}, volume={206}, pages={603-637} }

Abstract:We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra ? and the noncommutative torus. We show that the tachyon algebra of ? is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus. We construct the corresponding real spectral triples and determine their…

## 61 Citations

Strings, Noncommutative Geometry and the Size of the Target Space

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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…

Matrix D-brane dynamics, logarithmic operators, and quantization of noncommutative spacetime

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Noncommutative Gauge Fields on

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It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of M-theory to tori with constant background three-form field. This indicates that…

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- Physics, Mathematics
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It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of M-theory to tori with constant background three-form field. This indicates that…

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