Theta functions on Noncommutative T^4

Details Theta functions on Noncommutative T^4 Theta functions on Noncommutative T^4

2003-03-11

arxiv.org/abs/hep-th/0303091v2

J.Math.Phys. 45 (2004) 461-474

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LaTeX, references added, typos corrected, version to appear in J. Math. Phys

Scientific paper

10.1063/1.1629778

We construct the so-called theta vectors on noncommutative T^4, which correspond to the theta functions on commutative tori with complex structures. Following the method of Dieng and Schwarz, we first construct holomorphic connections and then find the functions satisfying the holomorphic conditions, the theta vectors. The holomorphic structure in the noncommutative T^4 case is given by a 2x2 complex matrix, and the consistency requires its off-diagonal elements to be the same. We also construct the tensor product of these functions satisfying the consistency requirement.

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