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

Journal Article · Fri Jan 22 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP01(2016)135· OSTI ID:1327303

Cvetič, M. ^[1]; Gibbons, G. W. ^[2]; Pope, C. N. ^[3]

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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

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.

• Research Organization: Univ. of Pennsylvania, Philadelphia, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0013528
• OSTI ID: 1327303
• Journal Information: Journal of High Energy Physics (Online), Vol. 2016, Issue 1; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
conformal field models in string theory
models of quantum gravity
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