Gravity duals of supersymmetric gauge theories on three-manifolds

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1) x U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.Comment: 74 pages, 2 figures; v2: minor change

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo

MicroRNA-222 regulates muscle alternative splicing through Rbm24 during differentiation of skeletal muscle cells

A number of microRNAs have been shown to regulate skeletal muscle development and differentiation. MicroRNA-222 is downregulated during myogenic differentiation and its overexpression leads to alteration of muscle differentiation process and specialized structures. By using RNA-induced silencing complex (RISC) pulldown followed by RNA sequencing, combined with in silico microRNA target prediction, we have identified two new targets of microRNA-222 involved in the regulation of myogenic differentiation, Ahnak and Rbm24. Specifically, the RNA-binding protein Rbm24 is a major regulator of muscle-specific alternative splicing and its downregulation by microRNA-222 results in defective exon inclusion impairing the production of muscle-specific isoforms of Coro6, Fxr1 and NACA transcripts. Reconstitution of normal levels of Rbm24 in cells overexpressing microRNA-222 rescues muscle-specific splicing. In conclusion, we have identified a new function of microRNA-222 leading to alteration of myogenic differentiation at the level of alternative splicing, and we provide evidence that this effect is mediated by Rbm24 protei

Multidomain switching in the ferroelectric nanodots

Controlling the polarization switching in the ferroelectric nanocrystals, nanowires and nanodots has an inherent specificity related to the emergence of depolarization field that is associated with the spontaneous polarization. This field splits the finite-size ferroelectric sample into polarization domains. Here, based on 3D numerical simulations, we study the formation of 180$^{\circ }$ polarization domains in a nanoplatelet, made of uniaxial ferroelectric material, and show that in addition to the polarized monodomain state, the multidomain structures, notably of stripe and cylindrical shapes, can arise and compete during the switching process. The multibit switching protocol between these configurations may be realized by temperature and field variations

The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six dimensions

We obtain necessary and sufficient conditions for a supersymmetric field configuration in the N=(1,0) U(1) or SU(2) gauged supergravities in six dimensions, and impose the field equations on this general ansatz. It is found that any supersymmetric solution is associated to an $SU(2)\ltimes \mathbb{R}^4$ structure. The structure is characterized by a null Killing vector which induces a natural 2+4 split of the six dimensional spacetime. A suitable combination of the field equations implies that the scalar curvature of the four dimensional Riemannian part, referred to as the base, obeys a second order differential equation. Bosonic fluxes introduce torsion terms that deform the $SU(2)\ltimes\mathbb{R}^4$ structure away from a covariantly constant one. The most general structure can be classified in terms of its intrinsic torsion. For a large class of solutions the gauge field strengths admit a simple geometrical interpretation: in the U(1) theory the base is K\"{a}hler, and the gauge field strength is the Ricci form; in the SU(2) theory, the gauge field strengths are identified with the curvatures of the left hand spin bundle of the base. We employ our general ansatz to construct new supersymmetric solutions; we show that the U(1) theory admits a symmetric Cahen-Wallach$_4\times S^2$ solution together with a compactifying pp-wave. The SU(2) theory admits a black string, whose near horizon limit is $AdS_3\times S_3$. We also obtain the Yang-Mills analogue of the Salam-Sezgin solution of the U(1) theory, namely $R^{1,2}\times S^3$, where the $S^3$ is supported by a sphaleron. Finally we obtain the additional constraints implied by enhanced supersymmetry, and discuss Penrose limits in the theories.Comment: 1+29 pages, late

Transceivers and Spectrum Usage Minimization in Few-Mode Optical Networks

Metro-Area networks are likely to create the right conditions for the deployment of few-mode transmission (FMT) due to limited metro distances and rapidly increasing metro traffic. To address the new network design problems arising with the adoption of FMT, integer linear programming (ILP) formulations have already been developed to optimally assign modulation formats, baud rates, and transmission modes to lightpaths, but these formulations lack scalability, especially when they incorporate accurate constraints to capture inter-modal coupling. In this paper, we propose a heuristic approach for the routing, modulation format, baud rate and spectrum allocation in FMT networks with arbitrary topology, accounting for inter-modal coupling and for distance-Adaptive reaches of few-mode (specifically, up to five modes) signals generated by either full multi-in multi-out (MIMO) or low-complexity MIMO transceivers and for two different switching scenarios (i.e., spatial full-joint and fractional-joint switching). In our illustrative numerical analysis, we first confirm the quasi-optimality of our heuristic by comparing it to the optimal ILP solutions, and then we use our heuristic to identify which switching scenario and FMT transceiver technology minimize spectrum occupation and transceiver costs, depending on the relative costs of transceiver equipment and dark fiber leasing

M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds

Seven-dimensional inhomogeneous Sasaki-Einstein manifolds $Y^{p,k}(KE_4)$ present a challenging example of AdS/CFT correspondence. At present, their field theory duals for $KE_4=\mathbb{CP}^2$ base are proposed only within a restricted range $3p/2\le k \le 2p$ as ${\cal N}=2$ quiver Chern-Simons-matter theories with $SU(N)\times SU(N)\times SU(N)$ gauge group, nine bifundamental chiral multiplets interacting through a cubic superpotential. To further elucidate this correspondence, we use particle approximation both at classical and quantum level. We setup a concrete AdS/CFT mapping of conserved quantities using geodesic motions, and turn to solutions of scalar Laplace equation in $Y^{p,k}$. The eigenmodes also provide an interesting subset of Kaluza-Klein spectrum for $D=11$ supergravity in ${\rm AdS}_4\times Y^{p,k}$, and are dual to protected operators written in terms of matter multiplets in the dual conformal field theory.Comment: v2 refs added. 19 pages 1 figur

Von Neumann's expanding model on random graphs

Within the framework of Von Neumann's expanding model, we study the maximum growth rate r achievable by an autocatalytic reaction network in which reactions involve a finite (fixed or fluctuating) number D of reagents. r is calculated numerically using a variant of the Minover algorithm, and analytically via the cavity method for disordered systems. As the ratio between the number of reactions and that of reagents increases the system passes from a contracting (r1). These results extend the scenario derived in the fully connected model (D\to\infinity), with the important difference that, generically, larger growth rates are achievable in the expanding phase for finite D and in more diluted networks. Moreover, the range of attainable values of r shrinks as the connectivity increases.Comment: 20 page