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.

AdS5 black strings in the stu model of FI-gauged N = 2 supergravity

“…Introducing the new radial coordinatê The central charge of the two-dimensional SCFT dual to the near-horizon configuration is given by [12,26] For the truncation φ 2 = 0, which means k + = 0, one has R AdS 3 = 2 −2/3 , i.e. the value found in [12].…”

“…It is worthwhile to note that with running hyperscalars the BPS equations, (5.17) of [26], can be simplified to a system for which the number of equations equals the number of the scalar fields in the model. The idea is basically the same as that of [3]: Introducing a new radial coordinate R by dR = e −ψ dr and the rescaled scalars y I = e ψ−2T h I , where ψ(r) and T (r) are metric functions defined in equ.…”

“…The idea is basically the same as that of [3]: Introducing a new radial coordinate R by dR = e −ψ dr and the rescaled scalars y I = e ψ−2T h I , where ψ(r) and T (r) are metric functions defined in equ. (3.1) of [26] and r denotes the radial coordinate used there, the system (5.17) of [26] boils down to ψ = 9κg 2 L y dR , e 3ψ−6T = 1 6 C IJK y I y J y K ,…”

Holographic microstate counting for AdS4 black holes in massive IIA supergravity

“…We refer the reader to[35][36][37][45][46][47][48][49] for a detailed analysis of superconformal theories obtained by twisted compactifications of four-dimensional N = 1 theories and their holographic realization.…”

Betti multiplets, flows across dimensions and c-extremization

“…Note added: when finishing this paper we noticed [29] on the ArXiv, where attractor equations for extremal black strings in presence of hypermultiplets have been derived via rewriting the action in a sum of squares, and a prescription to compute c 2d from 5d N = 2 gauged supergravity is provided.…”