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Extremal solutions of the S3 model and nilpotent orbits of G2(2)

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Abstract

We study extremal black hole solutions of the S3 model (obtained by setting S=T=U in the STU model) using group theoretical methods. Upon dimensional reduction over time, the S3 model exhibits the pseudo-Riemannian coset structure \( {{G} \left/ {{\tilde{K}}} \right.} \) with G = G2(2) and \( \tilde{K} = {\text{S}}{{\text{O}}_0}\left( {2,2} \right) \). We study nilpotent \( \tilde{K} \)-orbits of G2(2) corresponding to non-rotating single-center extremal solutions. We find six such distinct \( \tilde{K} \)-orbits. Three of these orbits are supersymmetric, one is non-supersymmetric, and two are unphysical. We write general solutions and discuss examples in all four physical orbits. We show that all solutions in supersymmetric orbits when uplifted to five-dimensional minimal supergravity have single-center Gibbons-Hawking space as their four-dimensional Euclidean hyper-Kähler base space. We construct hitherto unknown extremal (supersymmetric as well as non-supersymmetric) pressureless black strings of minimal five-dimensional supergravity and briefly discuss their relation to black rings.

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Authors and Affiliations

  1. Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050, Bruxelles, Belgium

    Sung-Soo Kim, Josef Lindman Hörnlund, Jakob Palmkvist & Amitabh Virmani

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  1. Sung-Soo Kim
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  2. Josef Lindman Hörnlund
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Correspondence to Jakob Palmkvist.

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ArXiv ePrint: 1004.5242

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Kim, SS., Lindman Hörnlund, J., Palmkvist, J. et al. Extremal solutions of the S3 model and nilpotent orbits of G2(2) . J. High Energ. Phys. 2010, 72 (2010). https://doi.org/10.1007/JHEP08(2010)072

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