Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the non-relativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.Comment: 4 page

Partition functions of chiral gauge theories on the two dimensional torus and their duality properties

Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An explicit computation of the partition functions shows that unitarity is recovered in particular regions of parameter space and that the effective dynamics is described in terms of fermionic interacting models. For the first family, this connection with fermionic models uncovers an exact duality which is conjectured to hold in the nonabelian case as well.Comment: RevTex, 13 pages, references adde

Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems

We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the respective eigenvectors. For binary logic using the truth values {0,1} logical observables are pairwise commuting projectors. For the truth values {+1,-1} the operator system is formally equivalent to that of a composite spin 1/2 system, the logical observables being isometries belonging to the Pauli group. Also in this approach fuzzy logic arises naturally when considering non-eigenvectors. The fuzzy membership function is obtained by the quantum mean value of the logical projector observable and turns out to be a probability measure in agreement with recent quantum cognition models. The analogy of many-valued logic with quantum angular momentum is then established. Logical observables for three-value logic are formulated as functions of the Lz observable of the orbital angular momentum l=1. The representative 3-valued 2-argument logical observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table

On the Topology of Black Hole Event Horizons in Higher Dimensions

In four dimensions the topology of the event horizon of an asymptotically flat stationary black hole is uniquely determined to be the two-sphere $S^2$. We consider the topology of event horizons in higher dimensions. First, we reconsider Hawking's theorem and show that the integrated Ricci scalar curvature with respect to the induced metric on the event horizon is positive also in higher dimensions. Using this and Thurston's geometric types classification of three-manifolds, we find that the only possible geometric types of event horizons in five dimensions are $S^3$ and $S^2 \times S^1$. In six dimensions we use the requirement that the horizon is cobordant to a four-sphere (topological censorship), Friedman's classification of topological four-manifolds and Donaldson's results on smooth four-manifolds, and show that simply connected event horizons are homeomorphic to $S^4$ or $S^2\times S^2$. We find allowed non-simply connected event horizons $S^3\times S^1$ and $S^2\times \Sigma_g$, and event horizons with finite non-abelian first homotopy group, whose universal cover is $S^4$. Finally, following Smale's results we discuss the classification in dimensions higher than six.Comment: 12 pages, minor edits 27/09/0

Exact Anomalous Dimensions for N=2 ADE SCFTs

We consider four-dimensional N=2 superconformal field theories based on ADE quiver diagrams. We use the procedure of hep-th/0206079 and compute the exact anomalous dimensions of operators with large U(1)_R charge to all orders in perturbation in the planar limit. The results are in agreement with the string computation in the dual pp-wave backgrounds.Comment: 8 pages, Latex2e. v2: two references added, some comments adde

Discussing controversial issues on social media : examining the role of affordances, fear of isolation and de-individuation

This dissertation sought to answer whether people more free to express their opinions on controversial topics on Twitter versus Facebook? Three specific affordances support this question: the networks people engage with on each platform, how identifiable they are to other users, and the visibility of their posts (Treem & Leonardi, 2012). In this dissertation, I draw from three related theoretical frameworks to support my argument: the spiral of silence (SOS), the social identity model of deindividuation effects (SIDE), and affordances theory. The results suggested that there were significant differences between Twitter and Facebook in terms of one’s willingness to express opinion. In summary people were more likely to express their opinion on Twitter than Facebook when they think the majority does not support their opinion.Journalis

The Infrared Einstein Ring in the Gravitational Lens MG1131+0456 and the Death of the Dusty Lens Hypothesis

We have obtained and modeled new NICMOS images of the lens system MG1131+0456, which show that its lens galaxy is an H=18.6 mag, transparent, early-type galaxy at a redshift of about z_l = 0.85; it has a major axis effective radius R_e=0.68+/-0.05 arcsec, projected axis ratio b/a=0.77+/-0.02, and major axis PA=60+/-2 degrees. The lens is the brightest member of a group of seven galaxies with similar R-I and I-H colors, and the two closest group members produce sufficient tidal perturbations to explain the ring morphology. The host galaxy of the MG1131+0456 source is a z_s > 2 ERO (``extremely red object'') which is lensed into optical and infrared rings of dramatically different morphologies. These differences imply a strongly wavelength-dependent source morphology that could be explained by embedding the host in a larger, dusty disk. At 1.6 micron (H), the ring is spectacularly luminous, with a total observed flux of H=17.4 mag and a de-magnified flux of 19.3 mag, corresponding to a 1-2L_* galaxy at the probable source redshift of z_s > 2. Thus, it is primarily the stellar emission of the radio source host galaxy that produces the overall colors of two of the reddest radio lenses, MG1131+0456 and B~1938+666, aided by the suppression of optical AGN emission by dust in the source galaxy. The dusty lens hypothesis -- that many massive early-type galaxies with 0.2 < z_l < 1.0 have large, uniform dust opacities -- is ruled out.Comment: 27 pages, 8 COLOR figures, submitted to ApJ. Black and white version available at http://cfa-www.harvard.edu/castle

Large Charge Four-Dimensional Extremal N=2 Black Holes with R^2-Terms

We consider N=2 supergravity in four dimensions with small R^2 curvature corrections. We construct large charge extremal supersymmetric and non-supersymmetric black hole solutions in all space, and analyze their thermodynamic properties.Comment: 18 pages. v2,3: minor fixe

The Pure Spinor Formulation of Superstrings

In this lectures we outline the construction of pure spinor superstrings. We consider both the open and closed pure spinor superstrings in critical and noncritical dimensions and on flat and curved target spaces with RR flux. We exhibit the integrability properties of pure spinor superstrings on curved backgrounds with RR fluxes.Comment: These lectures have been given in the RTN Winter School on Strings, Supergravity and Gauge Theories, CERN (2008). 32 pages, a typo correcte