2003/12/22 by J. Bellorin, Jorge Bellorín, Bellorin, J. +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0312265
arxiv created 2003/12/22 · openalex publication_date 2003/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the minimal configurations of the compact D=11 Supermembrane and D-branes when the spatial part of the world-volume is a Kähler manifold. The minima of the corresponding hamiltonians arise at immersions into the target space minimizing the Kähler volume. Minimal immersions of particular Kähler manifolds into a given target space are known to exist. They have associated to them a symplectic matrix of central charges. We reexpress the Hamiltonian of the D=11 Supermembrane with a symplectic matrix of central charges, in the light cone gauge, using the minimal immersions as backgrounds and the Sp\parent2g,ℤ symmetry of the resulting theory, g being the genus of the Kähler manifold. The resulting theory is a symplectic noncommutative Yang-Mills theory coupled with the scalar fields transverse to the Supermembrane. We prove that both theories are exactly equivalent. A similar construction may be performed for the Born-Infeld action. Finally, the noncommutative formulation is used to show that the spectrum of the reguralized Hamiltonian of the above mentioned D=11 Supermembrane is a discrete set of eigenvalues with finite multiplicity.