Matrix Representations of Holomorphic Curves on $T_4$

Abstract

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.

29 pages

References in corpus (7)

• Deformation quantization of Poisson manifolds, I
• Why is the Matrix Model Correct?
• Another Conjecture about M(atrix) Theory
• Matrix Theory
• Lectures on D-branes, Gauge Theory and M(atrices)
• Review of Matrix Theory
• Holomorphic curves from matrices

Cited by in corpus (7)

• Noncommutative Gravity
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Diffeomorphism covariant star products and noncommutative gravity
• A New Class of Two-Dimensional Noncommutative Spaces
• Tensor calculus on noncommutative spaces
• Quantum Mechanics on the Hypercube
• String with noncommutative world-sheet and stringy instantons