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) superconformal field theory (SCFT) that originates from a parent N= (4, 4) theory living on a D1-D5 system. This is achieved starting from the BPS black string in 6d with an AdS<inf>3</inf>×S³ attractor and taking two different routes to arrive at a 1/2 BPS AdS<inf>2</inf>×S² attractor of a non-BPS black hole in 4d N=2 flat gauged supergravity. The two inequivalent routes interchange the order of KK reduction on AdS<inf>3</inf> and SS reduction on S³. 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 I<inf>4</inf> to -I<inf>4</inf>.