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We extend the analysis of arXiv:0801.4457 [hep-th] to charged black hole solutions
of four-dimensional U(1)4 gauged supergravity which carry three charges. There
are two decoupling near-horizon limits, one over the near-BPS black hole solution
and the other over the near-extremal, but non-BPS geometry. Taking the limit
over the eleven dimensional uplift of these black hole solutions, for both of these
cases we obtain a geometry which has a piece (conformal) to rotating BTZ×S2.
We study the 4d, 11d and 5d, 3d black hole properties. Moreover, we show
that the BTZ×S2 geometry obtained after the near-BPS (near-extremal) limit is
also a solution to five-dimensional U(1)3 un-gauged (gauged) STU supergravity.
Based on these decoupling limits we argue that there should be sectors of 3d
CFT resulting from low energy limit of theory on N M2-branes (N ! 1), which
are decoupled from the rest of the theory and are effectively described by a 2d
CFT. The central charge of the 2d CFT in both near-BPS and near-extremal
case scales as N. The engineering dimension of the operators in these decoupled
sectors scales as N4/3 (for near-BPS case) while as N3/2 (for the near-extremal
case). Moreover, we discuss the description of the decoupled sectors as certain
deformations of 6d CFT residing on the intersecting M5-brane giants.
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