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Title: Compactifications of deformed conifolds, branes and the geometry of qubits $\mathfrak S

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 CPn+1, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V2($$\mathbb R^{2+3}$$) = SO(n+2)/SO(n) divided by Z2. The second family are also Einstein-Kahler metrics, now on the Grassmannian manifolds G2(Rn+3) = SO(n+3)/((SO(n+1)×SO(2)), whose principal orbits are the Stiefel manifolds V2($$\mathbb R^{2+3}$$) (with no Z2 factoring in this case). Furthermore, the third family are Einstein metrics on the product manifolds Sn+1 × Sn+1, and are Kahler 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. Also, we elaborate on the geometric approach to quantum mechanics based on the Kahler geometry of Fubini-Study metrics on $$\mathbb CP^{n+1}$$, and we apply the formalism to study the quantum entanglement of qubits.
Authors:
 [1] ;  [2] ;  [3]
  1. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics
  2. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; Cambridge Univ. (United Kingdom). Center for Mathematiclal Sciences; Univ. of Franc-Rabelais Tours (France). Lab. of Mathematics and Physics; Loire Valley Inst. for Advanced Studies, Tours (France)
  3. Cambridge Univ. (United Kingdom). Center for Mathematiclal Sciences; Univ. of Franc-Rabelais Tours (France). Lab. of Mathematics and Physics
Publication Date:
OSTI Identifier:
1327303
Grant/Contract Number:
SC0013528
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal field models in string theory; models of quantum gravity; differential and algebraic geometry