6d → 5d → 4d reduction of BPS attractors in flat gauged supergravities

Via a series of Kaluza–Klein (KK) and Scherk–Schwarz (SS) compactifications we relate BPS attractors and their complete (in general non-BPS) flows to a Minkowski vacuum in gauged supergravities with vanishing scalar potential in 4, 5, and 6 dimensions. This way we can look at a class of extremal non-BPS black holes and strings from IIB string theory viewpoint, keeping 4 supercharges on the horizon. Our results imply the existence of a dual 2d N=(0,2)N=(0,2) superconformal field theory (SCFT) that originates from a parent N=(4,4)N=(4,4) theory living on a D1–D5 system.This is achieved starting from the BPS black string in 6d with an AdS3×S3AdS3×S3 attractor and taking two different routes to arrive at a 1/2 BPS AdS2×S2AdS2×S2 attractor of a non-BPS black hole in 4d N=2N=2 flat gauged supergravity. The two inequivalent routes interchange the order of KK reduction on AdS3AdS3 and SS reduction on S3S3. We also find the commutator between the two operations after performing a duality transformation: on the level of the theory the result is the exchange of electric with magnetic gaugings; on the level of the solution we find a flip of the quartic invariant I4I4 to −I4−I4.