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We extend the analysis of arXiv:0801.4457 [hep-th] to charged black holesolutions of four-dimensional $U(1)^4$ gauged supergravity which carry threecharges. There are two decoupling near-horizon limits, one over the near-BPSblack hole solution and the other over the near-extremal, but non-BPS geometry.Taking the limit over the eleven dimensional uplift of these black holesolutions, for both of these cases we obtain a geometry which has a piece(conformal) to rotating BTZ $\times S^2$. We study the 4d, $11d$ and $5d, 3d$black hole properties. Moreover, we show that the BTZ$\times S^2$ geometryobtained after the near-BPS (near-extremal) limit is also a solution tofive-dimensional $U(1)^3$ un-gauged (gauged) STU supergravity. Based on thesedecoupling limits we argue that there should be sectors of 3d CFT resultingfrom low energy limit of theory on $N$ M2-branes ($N\to \infty)$, which aredecoupled from the rest of the theory and are effectively described by a 2dCFT. The central charge of the 2d CFT in both near-BPS and near-extremal casescales as $N$. The engineering dimension of the operators in these decoupledsectors scales as $N^{4/3}$ (for near-BPS case) while as $N^{3/2}$ (for thenear-extremal case). Moreover, we discuss the description of the decoupledsectors as certain deformations of $6d$ CFT residing on the intersectingM5-brane giants.

Nearing 11d Extremal Intersecting Giants and New Decoupled Sectors in D = 3,6 SCFT's