SO(d, d; Z) Transformation Property for Gauge Fluxes and Ramond-Ramond Fields in Noncommutative Geom

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In this paper we study the spinor constructions of gauge fluxes and Ramond Ramond fields on noncommu-tative tori Td up to d=6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced.So that we can express the Chern Simons Lagrangian in toroidal compactification as a product of spinors.
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