A Massive Study of M2-brane Proposals

We test the proposals for the worldvolume theory of M2-branes by studying its maximally supersymmetric mass-deformation. We check the simplest prediction for the mass-deformed theory on N M2-branes: that there should be a set of discrete vacua in one-to-one correspondence with partitions on N. For the mass-deformed Lorentzian three-algebra theory, we find only a single classical vacuum, casting doubt on its M2-brane interpretation. For the mass-deformed ABJM theory, we do find a discrete set of solutions, but these are more numerous than predicted. We discuss possible resolutions of this puzzling discrepancy. We argue that the classical vacuum solutions of the mass-deformed ABJM theory display properties of fuzzy three-spheres, as expected from their gravitational dual interpretation.Comment: 33 pages, LaTeX; references and acknowledgment adde

M5 spikes and operators in the HVZ membrane theory

In this note we study some aspects of the so-called dual ABJM theory introduced by Hanany, Vegh & Zaffaroni. We analyze the spectrum of chiral operators, and compare it with the spectrum of functions on the mesonic moduli space M=C^2\times C^2/Z_k, finding expected agreement for the coherent branch. A somewhat mysterious extra branch of dimension N^2 opens up at the orbifold fixed point. We also study BPS solutions which represent M2/M5 intersections. The mesonic moduli space suggests that there should be two versions of this spike: one where the M5 lives in the orbifolded C^2 and another where it lives in the unorbifolded one. While expectedly the first class turns out to be like the ABJM spike, the latter class looks like a collection of stacks of M5 branes with fuzzy S^3 profiles. This shows hints of the appearance of the global SO(4) at the non-abelian level which is otherwise not present in the bosonic potential. We also study the matching of SUGRA modes with operators in the coherent branch of the moduli space. As a byproduct, we present some formulae for the laplacian in conical CY_4 of the form C^n\times CY_{4-n}.Comment: 22 pages, 1 figure. Published version with corrected typos

Twistors, CFT and Holography

According to one of many equivalent definitions of twistors a (null) twistor is a null geodesic in Minkowski spacetime. Null geodesics can intersect at points (events). The idea of Penrose was to think of a spacetime point as a derived concept: points are obtained by considering the incidence of twistors. One needs two twistors to obtain a point. Twistor is thus a ``square root'' of a point. In the present paper we entertain the idea of quantizing the space of twistors. Twistors, and thus also spacetime points become operators acting in a certain Hilbert space. The algebra of functions on spacetime becomes an operator algebra. We are therefore led to the realm of non-commutative geometry. This non-commutative geometry turns out to be related to conformal field theory and holography. Our construction sheds an interesting new light on bulk/boundary dualities.Comment: 21 pages, figure

The baryon vertex with magnetic flux

In this letter we generalise the baryon vertex configuration of AdS/CFT by adding a suitable instantonic magnetic field on its worldvolume, dissolving D-string charge. A careful analysis of the configuration shows that there is an upper bound on the number of dissolved strings. This should be a manifestation of the stringy exclusion principle. We provide a microscopical description of this configuration in terms of a dielectric effect for the dissolved strings.Comment: 17 pages, 2 figures. V2: reference added. V3: version to appear in JHE

Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves

We characterize the worldvolume theories on symmetric D-branes in a six-dimensional Cahen-Wallach pp-wave supported by a constant Neveu-Schwarz three-form flux. We find a class of flat noncommutative euclidean D3-branes analogous to branes in a constant magnetic field, as well as curved noncommutative lorentzian D3-branes analogous to branes in an electric background. In the former case the noncommutative field theory on the branes is constructed from first principles, related to dynamics of fuzzy spheres in the worldvolumes, and used to analyse the flat space limits of the string theory. The worldvolume theories on all other symmetric branes in the background are local field theories. The physical origins of all these theories are described through the interplay between isometric embeddings of branes in the spacetime and the Penrose-Gueven limit of AdS3 x S3 with Neveu-Schwarz three-form flux. The noncommutative field theory of a non-symmetric spacetime-filling D-brane is also constructed, giving a spatially varying but time-independent noncommutativity analogous to that of the Dolan-Nappi model.Comment: 52 pages; v2: References adde

Conjunctions of social categories considered from different points of view

Conjunctions of divergent social categories may elicit emergent attributes to render the composite concept more coherent. Following Kunda, Miller & Clare, (1990) participants listed and rated attributes for people who belong to unexpected conjunctions of social categories. In order to explore the flexibility in such constructions, they were also asked to adopt the point of view of a person in one of the two categories. Experiment 1 found that when adopting the point of view of one constituent category, people tended to combine the concepts antagonistically, meaning that they attributed to members of the conjunction the more negative aspects of the opposing category. Experiment 2 showed that this polarizing effect was reduced when the point of view category was itself unusual. Strong gender stereotype differences were also found in the degree to which combinations were antagonistic. Female stereotypes as points of view generated a greater degree of integration in the conceptual combination

Extensions of algebraic image operators: An approach to model-based vision

Researchers extend their previous research on a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, researchers devised an innovative, efficient edge detection scheme. An accurate method for deriving gradient component information from this edge detector is presented. Based upon this new edge detection system researchers developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The algebraic operators are global operations which are easily reconfigured to operate on any size or shape region. This provides a natural platform from which to pursue dynamic scene analysis. A method for optimizing the linear feature extractor which capitalizes on the spatially reconfiguration nature of the edge detector/gradient component operator is discussed