2008/03/24 by M. P. Garcia del Moral, M.P. Garcıa del Moral, J. M. Pena +2
Physics and Astronomy · #Black Holes and Theoretical Physics #Central charge #Compactification (mathematics) #Hamiltonian (control theory) #Holomorphic function #Homogeneous space #Minkowski space #Moduli space #Quantum Mechanics and Non-Hermitian Physics #Riemann surface #Supersymmetry #Topological Materials and Phenomena #hep-th
paper · pdf · doi:10.1002/prop.200810548
published as Fortschr.Phys.56:915-921,2008 · 6pg.latex, w-art.class. To appear in the proceedings "RTN ForcesUniverse" Valencia, 1-5 October, Spain, 2007
arxiv created 2008/03/24 · openalex publication_date 2008/07/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract In this note we summarize some of the properties found in [1], and its relation with [2]. We comment on the construction of the action of the 11D supermembrane with nontrivial central charges minimally immersed on a 7D toroidal manifold is obtained (MIM2).The transverse coordinates to the supermembrane are maps to a 4D Minkowski space‐time. The action is invariant under additional symmetries in comparison to the supermembrane on a 11D Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N = 1 supermultiplet. When assuming the target‐space to be an isotropic 7‐tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters. Moreover due to the discrete symmetries of the hamiltonian, there are only 7 possible minimal holomorphic immersions of the MIM2 on the 7‐torus. When these symmetries are identified on the target space, it corresponds to compactify the MIM2 on a orbifold with G2 structure. Once the singularities are resolved it leads to the compactification of the MIM2 on a G2 manifold as shown in [2].