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arXiv 0802.1659hep-th
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5D黑洞与非线性西格玛模型

5D Black Holes and Non-linear Sigma Models

Micha Berkooz, Boris Pioline

摘要:

具有U(1)等距性的5D超引力定常解可以通过降维到三维来有效地研究,在三维中它们可以降维到局部超对称非线性西格玛模型的解。我们将这个过程推广到5D规范超引力,并确定相应的3D规范。我们特别注意的情况下,Killing旋量沿纤维化是不恒定的,这导致,即使在5D的未规范的超引力,在一个额外的测量在3D中,而不引入任何额外的潜力。我们进一步研究了SU(2)\times U(1)对称解,它对应于西格玛模型上的测地线运动(在规范情形下有势).我们识别并研究了Breckenridge-Myers-Peet-Vafa黑洞、Gutowski-Reall黑洞和其他几个BPS解的BPS约束代数,并在半经典近似下得到了相应的径向波函数.

英文摘要:

Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric non-linear sigma model. We generalize this procedure to 5D gauged supergravity, and identify the corresponding gauging in 3D. We pay particular attention to the case where the Killing spinor is non constant along the fibration, which results, even for ungauged supergravity in 5D, in an additional gauging in 3D, without introducing any extra potential. We further study SU(2)\times U(1) symmetric solutions, which correspond to geodesic motion on the sigma model (with potential in the gauged case). We identify and study the algebra of BPS constraints relevant for the Breckenridge-Myers-Peet-Vafa black hole, the Gutowski-Reall black hole and several other BPS solutions, and obtain the corresponding radial wave functions in the semi-classical approximation.

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