supersymmetric black attractors in six and seven dimensions

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• 作者：A. Belhaj ; L.B. Drissi ; E.H. Saidi ; A. Segui
• 关键词：Type IIA superstring on the K3 surface ; Special hyper-K&#xe4 ; hler geometry ; 6D/7D me="mml22">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml22&_user=1067359&_cdi=5531&_rdoc=6&_acct=C00005022
• 刊名：Nuclear Physics B
• 出版年：2008
• 期刊代码：45_05503213
• 类别：ph
• 出版时间：21 June 2008
• 卷：796
• 期：3
• 页码：521-580
• 文件大小：483 K

摘要

Using a quaternionic formulation of the moduli space M me="mml2">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml2&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=f5262c15fa8f6a6f7d6b22121d1f5655" title="Click to view the MathML source" alt="Click to view the MathML source">(IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume me="mml3">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml3&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=ca06ee421a4b5e92d05e343637f8c9fc" title="Click to view the MathML source" alt="Click to view the MathML source">V₀, we study extremal me="mml4">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml4&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=b8f183d223919bbf881bedc5c666a4ac">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-199/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=14 width="46"/> black attractors in 6D space–time and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D me="mml5">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml5&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=9bf30c4bd87ccf95b04d5a20baab563e">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-YR/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=14 width="45"/> hypermultiplets and the me="mml6">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml6&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=92a886f3ea0b7c47a94a12ba431a855b" title="Click to view the MathML source" alt="Click to view the MathML source">Z^m central charges isotriplet of the 6D me="mml7">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml7&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=0248d170ed34a2a7519b544796b99f1a">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-1R6/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=14 width="46"/> superalgebra. We construct explicitly the special hyper-Kähler geometry of M me="mml8">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml8&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=4c0d8087cb46b63eaa1b6b5d5a340873" title="Click to view the MathML source" alt="Click to view the MathML source">(IIA/K3) and show that the me="mml9">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml9&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=a80bddf440388b53ec166aed4f7071a8" title="Click to view the MathML source" alt="Click to view the MathML source">SO(4)×SO(20) invariant hyper-Kähler potential is given by me="mml10">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml10&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=050bde56ca5b446d139019f39ca1e53b">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-3/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=21 width="189"/> with Kähler leading term me="mml11">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml11&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=f7bae89d4172bf602e98d96a9e730303">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-42/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=15 width="100"/> plus an extra term which can be expanded as a power series in me="mml12">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml12&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=d3f5454ec3e2c48411d9d7cf977c52ac">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-81/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=21 width="28"/> and the traceless and symmetric 3×3 matrix S. We also derive the holomorphic matrix prepotential me="mml13">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml13&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=c8431b9bfe027f7aaddb187bbccb4b39">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-D0/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=14 width="11"/> and the flux potential me="mml14">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml14&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=0485c3dfc92d526bb8e3eeefc4ebf2d9">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-HY/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=15 width="28"/> of the 6D black objects induced by the topology of the RR field strengths me="mml15">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml15&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=ad217e9ff9a7a63a0458534a0baf52e2">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-NX/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=15 width="67"/> and me="mml16">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml16&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=dc22e99bf941d90d73746d800c175263">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-TW/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=15 width="68"/> on the K3 surface and show that me="mml17">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml17&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=07ae94fff522a29bcfd8b5ba48ded99c">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-VV/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=15 width="28"/> reads as me="mml18">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml18&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=28dd40a78b47d7081044ee9f114e73b6">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-W7/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=21 width="125"/>. Moreover, we reveal that me="mml19">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml19&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=0e45db832a7f79f5be1b2fcd6fe07c5e">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-WM/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=26 width="162"/> where the isotriplet me="mml20">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml20&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=321946d4a67e4b5af2c60f948800b3db" title="Click to view the MathML source" alt="Click to view the MathML source">J^m is the hyper-Kähler 2-form on the K3 surface. It is found as well that the uplifting to seven dimensions is quite similar to 4D/5D correspondence for back hole potential considered in arXiv: 0707.0964 [hep-ph]. Then we study the me="mml21">method=retrieve&_udi=B6TVC-4RC2NMM-2&_mathId=mml21&_user=1067359&_cdi=5531&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=3f6286460c1ab23a400eef4a6a021ffa">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4RC2NMM-2-XF/0?wchp=dGLbVtz-zSkWW" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=14 width="46"/> black object attractors in 6D and 7D obtained respectively from type IIA string and M-theory on K3.