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

Cvetič, M.; Gibbons, G. W.; Pope, C. N.

doi:10.1007/JHEP01(2016)135

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

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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 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:

Cvetič, M. ^[1]; Gibbons, G. W. ^[2]; Pope, C. N. ^[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 Franc-Rabelais 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 Franc-Rabelais Tours (France). Lab. of Mathematics and Physics

Publication Date:: Fri Jan 22 00:00:00 EST 2016

Research Org.:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1327303

Grant/Contract Number:: SC0013528

Resource 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

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

Citation Formats


                    Cvetič, M., Gibbons, G. W., and Pope, C. N. Compactifications of deformed conifolds, branes and the geometry of qubits $\mathfrak S.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP01(2016)135.

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                    Cvetič, M., Gibbons, G. W., & Pope, C. N. Compactifications of deformed conifolds, branes and the geometry of qubits $\mathfrak S.  United States.  https://doi.org/10.1007/JHEP01(2016)135

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                    Cvetič, M., Gibbons, G. W., and Pope, C. N. Fri .  
"Compactifications of deformed conifolds, branes and the geometry of qubits $\mathfrak S".  United States.  https://doi.org/10.1007/JHEP01(2016)135.  https://www.osti.gov/servlets/purl/1327303.

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@article{osti_1327303,

  title        = {Compactifications of deformed conifolds, branes and the geometry of qubits $\mathfrak S},

  author       = {Cvetič, M. and Gibbons, G. W. and Pope, C. N.},

  abstractNote = {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.},

  doi          = {10.1007/JHEP01(2016)135},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 1,

  volume       = 2016,

  place        = {United States},

  year         = {Fri Jan 22 00:00:00 EST 2016},

  month        = {Fri Jan 22 00:00:00 EST 2016}

}

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