Matrix Representations of Holomorphic Curves on $T_{4}$

Details Matrix Representations of Holomorphic Curves on $T_{4}$ Matrix Representations of Holomorphic Curves on $T_{4}$

1998-12-20

arxiv.org/abs/hep-th/9812184v1

JHEP 0008 (2000) 047

Physics

High Energy Physics

High Energy Physics - Theory

29 pages

Scientific paper

10.1088/1126-6708/2000/08/047

We construct a matrix representation of compact membranes analytically embedded in complex tori. Brane configurations give rise, via Bergman quantization, to U(N) gauge fields on the dual torus, with almost-anti-self-dual field strength. The corresponding U(N) principal bundles are shown to be non-trivial, with vanishing instanton number and first Chern class corresponding to the homology class of the membrane embedded in the original torus. In the course of the investigation, we show that the proposed quantization scheme naturally provides an associative star-product over the space of functions on the surface, for which we give an explicit and coordinate-invariant expression. This product can, in turn, be used the quantize, in the sense of deformation quantization, any symplectic manifold of dimension two.

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