Compactifications of deformed conifolds, branes and the geometry of qubits $\mathfrak S
We present three families of exact, cohomogeneityone Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricciflat metrics to those with a positive cosmological constant. The first family of solutions are FubiniStudy metrics on the complex projective spaces CP ^{n+1}, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V _{2}($$\mathbb R^{2+3}$$) = SO(n+2)/SO(n) divided by Z _{2}. The second family are also EinsteinKahler metrics, now on the Grassmannian manifolds G _{2}(R ^{n+3}) = SO(n+3)/((SO(n+1)×SO(2)), whose principal orbits are the Stiefel manifolds V _{2}($$\mathbb R^{2+3}$$) (with no Z _{2} factoring in this case). Furthermore, the third family are Einstein metrics on the product manifolds S ^{n+1} × S ^{n+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 FubiniStudy metrics on $$\mathbb CP^{n+1}$$, and we apply the formalism to study the quantum entanglement of qubits.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics
 Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; Cambridge Univ. (United Kingdom). Center for Mathematiclal Sciences; Univ. of FrancRabelais Tours (France). Lab. of Mathematics and Physics; Loire Valley Inst. for Advanced Studies, Tours (France)
 Cambridge Univ. (United Kingdom). Center for Mathematiclal Sciences; Univ. of FrancRabelais 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 10298479
 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
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