We study near-horizon limits of near-extremal charged black hole solutions to five-dimensional U(1) 3 gauged supergravity carrying two charges, extending the recent work of Balasubramanian et.al. [1]. We show that there are two nearhorizon decoupling limits for the near-extremal black holes, one corresponding to the near-BPS case and the other for the far from BPS case. Both of these limits are only defined on the 10d IIB uplift of the 5d black holes, resulting in a decoupled geometry with a six-dimensional part (conformal to) a rotating BTZ×S 3 . We study various aspects of these decoupling limits both from the gravity side and the dual field theory side. For the latter we argue that there should be two different, but equivalent, dual gauge theory descriptions, one in terms of the 2d CFT's dual to the rotating BTZ and the other as certain large R-charge sectors of d = 4, N = 4 U(N) SYM theory. We discuss new BMNtype sectors of the N = 4 SYM in the N → ∞ limit in which the engineering dimensions scale as N 3/2 (for the near-BPS case) and as N 2 (for the far from BPS case). Introduction and SummaryAccording to AdS/CFT conjecture [2, 3] any state/physical process in the asymptotically AdS 5 × S 5 geometry can be described by a (perturbative) deformation of N = 4, d = 4 supersymmetric Yang-Mills (SYM) theory. A class of deformations of AdS 5 ×S 5 are solutions to N = 2, d = 5 U(1) 3 gauged supergravity (the "gauged STU model"), for a review e.g. see [4,5]). Among these solutions there are geometries carrying charges under some (or all) of the three U(1)'s. These are generically 5d black hole type solutions. It is possible to uplift these solutions to 10d and obtain the corresponding type IIB solutions which are constant dilaton solutions only involving metric and the (self-dual) five-form field of IIB theory. These solutions which have been extensively studied from the gravity viewpoint (e.g. see [5] and references therein) can be 1/2, 1/4, 1/8 BPS respectively preserving 16, 8, 4 supercharges. The 10d BPS solutions have been called superstars [6].In the 10d picture the 1/2 BPS solutions correspond to smeared (delocalized) spherical D3-branes [6], the giant gravitons [7]. These are branes wrapping a three sphere inside the S 5 part of the background AdS 5 × S 5 geometry while moving on a geodesic along an S 1 ∈ S 5 transverse to the worldvolume S 3 and smeared (delocalized) over the remaining direction. The 1/2 BPS solutions are specified by a single parameter, the value of the charge. In a similar manner the two-charge 1/4 BPS and three-charge 1/8 BPS solutions can be understood as geometries corresponding to intersecting giant gravitons. The nonsupersymmetric cases then correspond to turning on specific open string excitations on the supersymmetric (intersecting) giant gravitons. Besides the (excited intersecting) spherical brane picture the 5d charged black hole type solutions should also have a description in the N = 4 SYM on R × S 3 . The 1/2 BPS case is described by chiral primary operators in the subdetermina...

In this paper we elaborate on the correspondence between the quantum Hall system with filling factor equal to one and the N = 4 SYM theory in the 1/2 BPS sector, previously mentioned in the [hep-th/0409174, 0409115]. We show the equivalence of the two in various formulations of the quantum Hall physics. We present an extension of the noncommutative Chern-Simons Matrix theory which contains independent degrees of freedom (fields) for particles and quasiholes. The BPS configurations of our model, which is a model with explicit particle-quasihole symmetry, are in one-to-one correspondence with the 1/2 BPS states in the N = 4 SYM. Within our model we shed light on some less clear aspects of the physics of the N = 4 theory in the 1/2 BPS sector, like the giant dual-giant symmetry, stability of the giant gravitons, and stringy exclusion principle and possible implications of the (fractional) quantum Hall effect for the AdS/CFT correspondence.

We find a new class of spiky solutions for closed strings in flat, AdS 3 ⊂ AdS 5 and R×S 2 (⊂ S 5 ) backgrounds. In the flat case the new solutions turn out to be T-dual configurations of spiky strings found in [15]. In the case of solutions living in AdS, we make a semi classical analysis by taking the large angular momentum limit. The anomalous dimension for these dual spikes is similar to that for rotating and pulsating circular strings in AdS with angular momentum playing the role of the level number. This replaces the well known logarithmic dependence for spinning strings. For the dual spikes living on sphere we find that no large angular momentum limit exists.

We study multiwrapped circular string pulsating in the radial direction of AdS black hole. We compute the energy of this string as a function of a large quantum number n. One then could associate it with energy and a quantum number of states in the dual finite temperature N = 4 SYM theory as well as three dimensional pure gauge theory. We observe that the n dependence of the energy has a universal form. We have also considered pulsating string in the background of the near-extremal D4-brane solution. Circular pulsating membrane in M-theory on AdS 7 × S 4 has also been studied.

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×S 2 . We study the 4d, 11d and 5d, 3d black hole properties. Moreover, we show that the BTZ×S 2 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 → ∞), 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 N 4/3 (for near-BPS case) while as N 3/2 (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.