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

TL;DR

The paper develops a Hamilton-Jacobi-based framework to obtain both BPS and non-BPS first-order flow equations for magnetically charged black strings in $N=2$, $d=5$ abelian gauged supergravity. It first treats FI gauging and vector multiplets, then includes hypermultiplets with abelian quaternionic gauging, deriving attractor equations for near-horizon geometries and, under an adjoint identity, closed-form horizon data and a central charge for the IR 2d CFT in terms of magnetic charges, FI parameters, and intersection numbers. An $r$-map is constructed to relate the five-dimensional flows to four-dimensional flows, unifying the 5d and 4d descriptions of holographic RG flows to 2d CFTs. The work provides explicit first-order flow equations, a charge-rotation method for non-BPS solutions, and exact attractor formulas, enabling detailed holographic analyses and setting the stage for extensions to nonextremal cases and running hypers. Overall, it offers a comprehensive 5d perspective on magnetically charged string solutions and their IR CFT data, with strong implications for holography and Calabi-Yau compactifications.

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.