First Results from Lattice Simulation of the PWMM

We present results of lattice simulations of the Plane Wave Matrix Model (PWMM). The PWMM is a theory of supersymmetric quantum mechanics that has a well-defined canonical ensemble. We simulate this theory by applying rational hybrid Monte Carlo techniques to a naive lattice action. We examine the strong coupling behaviour of the model focussing on the deconfinement transition.Comment: v3 20 pages, 8 figures, comment adde

Higher spin fermions in the BTZ black hole

Recently it has been shown that the wave equations of bosonic higher spin fields in the BTZ background can be solved exactly. In this work we extend this analysis to fermionic higher spin fields. We solve the wave equations for arbitrary half-integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. These quasinormal modes are shown to agree precisely with the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We also obtain an expression for the 1-loop determinant in terms of the quasinormal modes and show it agrees with that obtained by integrating the heat kernel found by group theoretic methods.Comment: 29 page

Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

Holographic flows to IR Lifshitz spacetimes

Recently we studied `vanishing' horizon limits of `boosted' black D3-brane geometry \cite{hsnr}. The type IIB solutions obtained by taking these special double limits were found to describe nonrelativistic Lifshitz spacetimes at zero temperature. In the present work we study these limits for TsT black-hole solutions which include $B$-field. The new Galilean solutions describe a holographic RG flow from Schr\"odinger ($a=2$) spacetime in UV to a Lifshitz universe ($a=3$) in the IR.Comment: 10 pages; v2: A bad typo in eq.8 corrected; v3: Discussion and reference on Kaigorodov spaces included, correction in sec-3, to be published in JHE

D-Branes on the Conifold and N=1 Gauge/Gravity Dualities

We review extensions of the AdS/CFT correspondence to gauge/ gravity dualities with N=1 supersymmetry. In particular, we describe the gauge/gravity dualities that emerge from placing D3-branes at the apex of the conifold. We consider first the conformal case, with discussions of chiral primary operators and wrapped D-branes. Next, we break the conformal symmetry by adding a stack of partially wrapped D5-branes to the system, changing the gauge group and introducing a logarithmic renormalization group flow. In the gravity dual, the effect of these wrapped D5-branes is to turn on the flux of 3-form field strengths. The associated RR 2-form potential breaks the U(1) R-symmetry to $Z_{2M}$ and we study this phenomenon in detail. This extra flux also leads to deformation of the cone near the apex, which describes the chiral symmetry breaking and confinement in the dual gauge theory.Comment: Based on I.R.K.'s lectures at the Les Houches Summer School Session 76, ``Gravity, Gauge Theories, and Strings'', August 2001, 42 pages, v2: clarifications and references adde

Spinning strings and integrable spin chains in the AdS/CFT correspondence

In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S^5. The energies of the folded and circular spinning string solutions rotating on a S^3 within the S^5 are derived, which yield all loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of N=4 super Yang-Mills in a minimal SU(2) subsector and we display its reformulation in terms of a Heisenberg s=1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies and the implications of this are discussed. Along the way we comment on further developments and generalizations of the subject and point to the relevant literature.Comment: 40 pages, invited contribution to Living Reviews in Relativity. v2: improvements in the text and references adde

Enhanced mitochondrial superoxide scavenging does not Improve muscle insulin action in the high fat-fed mouse

Improving mitochondrial oxidant scavenging may be a viable strategy for the treatment of insulin resistance and diabetes. Mice overexpressing the mitochondrial matrix isoform of superoxide dismutase (sod2(tg) mice) and/or transgenically expressing catalase within the mitochondrial matrix (mcat(tg) mice) have increased scavenging of O2(˙-) and H2O2, respectively. Furthermore, muscle insulin action is partially preserved in high fat (HF)-fed mcat(tg) mice. The goal of the current study was to test the hypothesis that increased O2(˙-) scavenging alone or in combination with increased H2O2 scavenging (mtAO mice) enhances in vivo muscle insulin action in the HF-fed mouse. Insulin action was examined in conscious, unrestrained and unstressed wild type (WT), sod2(tg), mcat(tg) and mtAO mice using hyperinsulinemic-euglycemic clamps (insulin clamps) combined with radioactive glucose tracers following sixteen weeks of normal chow or HF (60% calories from fat) feeding. Glucose infusion rates, whole body glucose disappearance, and muscle glucose uptake during the insulin clamp were similar in chow- and HF-fed WT and sod2(tg) mice. Consistent with our previous work, HF-fed mcat(tg) mice had improved muscle insulin action, however, an additive effect was not seen in mtAO mice. Insulin-stimulated Akt phosphorylation in muscle from clamped mice was consistent with glucose flux measurements. These results demonstrate that increased O2(˙-) scavenging does not improve muscle insulin action in the HF-fed mouse alone or when coupled to increased H2O2 scavenging

Holography of a Composite Inflaton

We study the time evolution of a brane construction that is holographically dual to a strongly coupled gauge theory that dynamically breaks a global symmetry through the generation of an effective composite Higgs vev. The D3/D7 system with a background magnetic field or non-trivial gauge coupling (dilaton) profile displays the symmetry breaking. We study motion of the D7 brane in the background of the D3 branes. For small field inflation in the field theory the effective Higgs vev rolls from zero to the true vacuum value. We study what phenomenological dilaton profile generates the slow rolling needed, hence learning how the strongly coupled gauge theory's coupling must run. We note that evolution of our configuration in the holographic direction, representing the phyiscs of the strong interactions, can provide additional slowing of the roll time. Inflation seems to be favoured if the coupling changes by only a small amount or very gently. We speculate on how such a scenario could be realized away from N=4 gauge theory, for example, in a walking gauge theory.Comment: 13 pages, 12 figures; v2: Added reference

Slab melting as a barrier to deep carbon subduction

Interactions between crustal and mantle reservoirs dominate the surface inventory of volatile elements over geological time, moderating atmospheric composition and maintaining a lifesupporting planet1. While volcanoes expel volatile components into surface reservoirs, subduction of oceanic crust is responsible for replenishment of mantle reservoirs2,3. Many natural, ‘superdeep’ diamonds originating in the deep upper mantle and transition zone host mineral inclusions, indicating an affinity to subducted oceanic crust4–7. Here we show that the majority of slab geotherms will intersect a deep depression along the melting curve of carbonated oceanic crust at depths of approximately 300 to 700 kilometres, creating a barrier to direct carbonate recycling into the deep mantle. Low-degree partial melts are alkaline carbonatites that are highly reactive with reduced ambient mantle, producing diamond. Many inclusions in superdeep diamonds are best explained by carbonate melt–peridotite reaction. A deep carbon barrier may dominate the recycling of carbon in the mantle and contribute to chemical and isotopic heterogeneity of the mantle reservoir

Nf2/Merlin controls spinal cord neural progenitor function in a Rac1/ErbB2-dependent manner

Objective: Individuals with the neurofibromatosis type 2 (NF2) cancer predisposition syndrome develop spinal cord glial tumors (ependymomas) that likely originate from neural progenitor cells. Whereas many spinal ependymomas exhibit indolent behavior, the only treatment option for clinically symptomatic tumors is surgery. In this regard, medical therapies are unfortunately lacking due to an incomplete understanding of the critical growth control pathways that govern the function of spinal cord (SC) neural progenitor cells (NPCs). Methods: To identify potential therapeutic targets for these tumors, we leveraged primary mouse Nf2-deficient spinal cord neural progenitor cells. Results: We demonstrate that the Nf2 protein, merlin, negatively regulates spinal neural progenitor cell survival and glial differentiation in an ErbB2-dependent manner, and that NF2-associated spinal ependymomas exhibit increased ErbB2 activation. Moreover, we show that Nf2-deficient SC NPC ErbB2 activation results from Rac1-mediated ErbB2 retention at the plasma membrane. Significance: Collectively, these findings establish ErbB2 as a potential rational therapeutic target for NF2-associated spinal ependymoma