Compactifications of deformed conifolds, branes and the geometry of qubits uri icon


  • 2016, The Author(s). Abstract: We present three families of exact, cohomogeneity-one Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces n+1, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V2(n+2)=SO(n+2)/SO(n) divided by 2. The second family are also Einstein-Khler metrics, now on the Grassmannian manifolds G2(n+3)=SO(n+3)/((SO(n+1)SO(2)), whose principal orbits are the Stiefel manifolds V2(n+2n+2 (with no 2 factoring in this case). The third family are Einstein metrics on the product manifolds Sn+1 Sn+1, and are Khler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the Khler geometry of Fubini-Study metrics on n+1, and we apply the formalism to study the quantum entanglement of qubits.

published proceedings


altmetric score

  • 1

author list (cited authors)

  • Cvetic, M., Gibbons, G. W., & Pope, C. N.

citation count

  • 0

complete list of authors

  • Cvetic, M||Gibbons, GW||Pope, CN