Black string first order flow in N=2, d=5 abelian gauged supergravity

Abstract

We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N=2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hypermultiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flow equations to those in four dimensions.

21 pages, uses jheppub.sty. v2: Minor errors corrected, refs. added. v3: Minor error corrected in app. B, small discussion of string theory realization added in final remarks

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• The Cardy limit of the topologically twisted index and black strings in AdS${}_5$
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• AdS${}_5$ black strings in the stu model of FI-gauged $N=2$ supergravity
• Supersymmetric $Ad{S}_5$ black holes and strings from 5D $N=4$ gauged supergravity
• Holographic RG flows and $Ad{S}_5$ black strings from 5D half-maximal gauged supergravity
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• Supersymmetric black holes with spiky horizons
• Rotating black holes with Nil or SL(2,$\mathbb{R}$) horizons
• Magnetically-charged supersymmetric flows of gauged $\mathcal{N}=8$ supergravity in five dimensions
• New supersymmetric $Ad{S}_5$ black strings from 5D $N=4$ gauged supergravity
• Higher order curvature corrections and holographic renormalization group flow
• Kerr-Newman black holes from $\mathcal{N}=1^{\ast }$
• Holographic solutions from 5D $SO(2)\times ISO(3)$ $N=4$ gauged supergravity