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...

We give a general framework for constructing supersymmetric solutions in the presence of non-trivial fluxes of tensor gauge fields. This technique involves making a general Ansatz for the metric and then defining the Killing spinors in terms of very simple projectors on the spinor fields. These projectors and, through them, the spinors, are determined algebraically in terms of the metric Ansatz. The Killing spinor equations then fix the tensor gauge fields algebraically, and, with the Bianchi identities, provide a system of equations for all the metric functions. We illustrate this by constructing an infinite family of massive flows that preserve eight supersymmetries in M -theory. This family constitutes all the radially symmetric Coulomb branch flows of the softly broken, large N scalar-fermion theory on M 2-branes. We reduce the problem to the solution of a single, non-linear partial differential equation in two variables. This equation governs the flow of the fermion mass, and the function that solves it then generates the entire M -theory solution algebraically in terms of the function and its first derivatives. While the governing equation is non-linear, it has a very simple perturbation theory from which one can see how the Coulomb branch is encoded.

We consider holographic RG flow solutions with eight supersymmetries and study the geometry transverse to the brane. For both M 2-branes and for D3-branes in F -theory this leads to an eight-manifold with only a fourform flux. In both settings there is a natural four-dimensional hyper-Kähler slice that appears on the Coulomb branch. In the IIB theory this hyperKähler manifold encodes the Seiberg-Witten coupling over the Coulomb branch of a U (1) probe theory. We focus primarily upon a new flow solution in M -theory. This solution is first obtained using gauged supergravity and then lifted to eleven dimensions. In this new solution, the brane probes have an Eguchi-Hanson moduli space with the M 2-branes spread over the non-trivial 2-sphere. It is also shown that the new solution is valid for a class of orbifold theories. We discuss how the hyper-Kähler structure on the slice extends to some form of G-structure in the eight-manifold, and describe how this can be computed. December, 2002

In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both the MLDE and the RCFT are identified by a pair of non-negative integers [n,l]. n is the number of characters of the RCFT as well as the order of the MLDE that the characters solve and l, the Wronskian index, is associated to the structure of the zeroes of the Wronskian of the characters. In this paper, we study [3,0] and [3,2] MLDEs in order to classify the corresponding CFTs. We reduce the problem to a “finite” problem: to classify CFTs with central charge 0 < c ≤ 96, we need to perform 6, 720 computations for the former and 20, 160 for the latter. Each computation involves (i) first finding a simultaneous solution to a pair of Diophantine equations and (ii) computing Fourier coefficients to a high order and checking for positivity.In the [3,0] case, for 0 < c ≤ 96, we obtain many character-like solutions: two infinite classes and a discrete set of 303. After accounting for various categories of known solutions, including Virasoro minimal models, WZW CFTs, Franc-Mason vertex operator algebras and Gaberdiel-Hampapura-Mukhi novel coset CFTs, we seem to have seven hitherto unknown character-like solutions which could potentially give new CFTs. We also classify [3,2] CFTs for 0 < c ≤ 96: each CFT in this case is obtained by adjoining a constant character to a [2,0] CFT, whose classification was achieved by Mathur-Mukhi-Sen three decades ago.