Mirror duality and noncommutative tori
@article{Kim2007MirrorDA, title={Mirror duality and noncommutative tori}, author={Eunsang Kim and Hoil Kim}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2007}, volume={42}, pages={015206} }
In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann conditions using mirror duality on ordinary complex tori. Based on this, we will find a mirror correspondence on generalized complex tori and generalize the mirror duality on complex tori to the case of noncommutative complex tori.
5 Citations
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References
SHOWING 1-10 OF 50 REFERENCES
A TOPOLOGICAL MIRROR SYMMETRY ON NONCOMMUTATIVE COMPLEX TWO-TORI
- Mathematics
- 2006
In this paper, we study a topological mirror symme- try on noncommutative complex tori. We show that deformation quantization of an elliptic curve is mirror symmetric to an irrational rotation…
Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Mathematics
- 1997
We study toroidal compactification of Matrix theory, using ideas and results of noncommutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification…
Non-commutative tori and Fourier–Mukai duality
- MathematicsCompositio Mathematica
- 2007
The classical Fourier–Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to…
Categories of Holomorphic Vector Bundles on Noncommutative Two-Tori
- Mathematics
- 2003
Abstract: In this paper we study the category of standard holomorphic vector bundles on a noncommutative two-torus. We construct a functor from the derived category of such bundles to the derived…
Kronecker foliation, D1 branes and Morita equivalence of noncommutative two tori
- Mathematics
- 2002
It is known that the physics of open strings on a D2-brane on a two-torus is realized from the viewpoint of deformation quantization in the Seiberg-Witten limit. We study its T-dual theory, i.e.…
Duality and equivalence of module categories in noncommutative geometry II: Mukai duality for holomorphic noncommutative tori
- Mathematics
- 2005
This is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In \cite{mem} we introduced the basic DG category…
Classification of Holomorphic Vector Bundles on Noncommutative Two-Tori
- Mathematics
- 2003
We prove that every holomorphic vector bundle on a noncommutative two-torus T can be obtained by successive exten- sions from standard holomorphic bundles considered in (2). This im- plies that the…
Theta Functions on Noncommutative Tori
- Mathematics
- 2001
Ordinary theta functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta functions as holomorphic elements of projective modules…