AdS${}_5$ black strings in the stu model of FI-gauged $N=2$ supergravity

Abstract

We analytically construct asymptotically AdS${}_5$ black string solutions starting from the four-dimensional domain wall black hole of arXiv:0911.4926. It is shown that its uplift gives a black string in $d=5$ minimal gauged supergravity, with momentum along the string. Applying instead the residual symmetries of $N=2$, $d=4$ Fayet-Iliopoulos-gauged supergravity discovered in arXiv:1606.05160 to the domain wall seed leads, after uplifting, to a dyonic black string that interpolates between AdS${}_5$ and ${\text{AdS}}_3\times {\text{H}}^2$ at the horizon. A Kaluza-Klein reduction of the latter along an angular Killing direction $\varphi$ followed by a duality transformation yields, after going back to five dimensions, a black string with both momentum along the string and rotation along $\varphi$. This is the first instance of using solution-generating techniques in gauged supergravity to add rotation to a given seed. These solutions all have constant scalar fields. As was shown in hep-th/0302218, the construction of supersymmetric static magnetic black strings in the FI-gauged stu model amounts to solving the $\text{SO}(2,1)$ spinning top equations, which descend from an inhomogeneous version of the Nahm equations. We are able to solve these in a particular case, which leads to a generalization of the Maldacena-Nuñez solution.

arXiv comment20 pages, uses jheppub.sty. v2: Refs. added. v3: Conclusions, some comments and further refs. added. Final version to appear in JHEP

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