Dilatation operator in (super-)Yang-Mills theories on the light-cone

The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal SU(2,2|N) symmetry should possess universal integrability properties for different N. We provide further support for this conjecture by computing a one-loop dilatation operator in all (super)symmetric Yang-Mills theories on the light-cone ranging from gluodynamics all the way to the maximally supersymmetric N=4 theory. We demonstrate that the dilatation operator takes a remarkably simple form when realized in the space spanned by single-trace products of superfields separated by light-like distances. The latter operators serve as generating functions for Wilson operators of the maximal Lorentz spin and the scale dependence of the two are in the one-to-one correspondence with each other. In the maximally supersymmetric, N=4 theory all nonlocal light-cone operators are built from a single CPT self-conjugated superfield while for N=0,1,2 one has to deal with two distinct superfields and distinguish three different types of such operators. We find that for the light-cone operators built from only one species of superfields, the one-loop dilatation operator takes the same, universal form in all SYM theories and it can be mapped in the multi-color limit into a Hamiltonian of the SL(2|N) Heisenberg (super)spin chain of length equal to the number of superfields involved. For "mixed'' light-cone operators involving both superfields the dilatation operator for N<=2 receives an additional contribution from the exchange interaction between superfields on the light-cone which breaks its integrability symmetry and creates a mass gap in the spectrum of anomalous dimensions.Comment: 70 pages, 3 figures; minor changes, references adde

Events and Processes in Language and Mind

Semantic theories predict that the dimension for comparison given a sentence like A gleebed more than B depends on what the verb gleeb means: if gleeb expresses a property of events, the evaluation should proceed by number; if it expresses a property of processes, any of distance, duration, or number should be available. An adequate test of theories like this requires first determining, independently of language, the conditions under which people will understand a novel verb to be true of a series of events or a single ongoing process. We investigate this prior question by studying people’s representation of two cues in simple visual scenes: a) whether some happening is interrupted by temporal pauses, and b) whether and how the speed of an object’s motion changes. We measured representation by probing people’s choice of verb in free-form descriptions of the scenes, and how they segment the scenes for the purposes of counting. We find evidence that both types of cues shape people’s representation of simple motions as events or processes, but in different ways

Self-assembly mechanism in colloids: perspectives from Statistical Physics

Motivated by recent experimental findings in chemical synthesis of colloidal particles, we draw an analogy between self-assembly processes occurring in biological systems (e.g. protein folding) and a new exciting possibility in the field of material science. We consider a self-assembly process whose elementary building blocks are decorated patchy colloids of various types, that spontaneously drive the system toward a unique and predetermined targeted macroscopic structure. To this aim, we discuss a simple theoretical model -- the Kern-Frenkel model -- describing a fluid of colloidal spherical particles with a pre-defined number and distribution of solvophobic and solvophilic regions on their surface. The solvophobic and solvophilic regions are described via a short-range square-well and a hard-sphere potentials, respectively. Integral equation and perturbation theories are presented to discuss structural and thermodynamical properties, with particular emphasis on the computation of the fluid-fluid (or gas-liquid) transition in the temperature-density plane. The model allows the description of both one and two attractive caps, as a function of the fraction of covered attractive surface, thus interpolating between a square-well and a hard-sphere fluid, upon changing the coverage. By comparison with Monte Carlo simulations, we assess the pros and the cons of both integral equation and perturbation theories in the present context of patchy colloids, where the computational effort for numerical simulations is rather demanding.Comment: 14 pages, 7 figures, Special issue for the SigmaPhi2011 conferenc

Hamiltonian for scalar field model of infinite derivative gravity

Theories with an infinite number of derivatives are described by non-local Lagrangians for which the standard Hamiltonian formalism cannot be applied. Hamiltonians of special types of non-local theories can be constructed by means of the (1+1)-dimensional Hamiltonian formalism. In this paper, we consider a simple scalar field model inspired by the infinite derivative gravity and study its reduced phase space by using this formalism. Assuming the expansion of the solutions in the coupling constant, we compute the perturbative Hamiltonian and the symplectic 2-form. We also discuss an example of a theory leading to an infinite-dimensional reduced phase space for a different choice of the form factor.Comment: 13 page

Automata network models of galaxy evolution

Two ideas appear frequently in theories of star formation and galaxy evolution: (1) star formation is nonlocally excitatory, stimulating star formation in neighboring regions by propagation of a dense fragmenting shell or the compression of preexisting clouds; and (2) star formation is nonlocally inhibitory, making H2 regions and explosions which can create low-density and/or high temperature regions and increase the macroscopic velocity dispersion of the cloudy gas. Since it is not possible, given the present state of hydrodynamic modeling, to estimate whether one of these effects greatly dominates the other, it is of interest to investigate the predicted spatial pattern of star formation and its temporal behavior in simple models which incorporate both effects in a controlled manner. The present work presents preliminary results of such a study which is based on lattice galaxy models with various types of nonlocal inhibitory and excitatory couplings of the local SFR to the gas density, temperature, and velocity field meant to model a number of theoretical suggestions

Modulating Emotion to Understand Prosocial Behavior

Reviews the book, Prosocial motives, emotions, and behavior: The better angels of our nature edited by Mario Mikulincer and Phillip R. Shaver This book serves as a well-organized primer for anyone interested in factors governing prosocial behaviors. Importantly, it also highlights why behaving prosocially is beneficial not only to the recipient but also to the provider, even when that deed is as simple as forgiveness. The broad goal of this book is to integrate what is known about prosocial behavior. The editors do a magnificent job making this edited work tell a cohesive story. In sum, this book does more than simply summarize types of prosocial motives, emotions, and behaviors. It provides a foundation for thinking about how to manage interpersonal, group, and perhaps societal (intergroup) relationships. Given our country’s military involvement abroad, it is refreshing to see work that highlights how we might attain positive social behavior. This book is relevant to a wide readership. It will appeal not only to social psychologists but also to any social scientist interested in human interactions. This includes those with interests in positive and health psychology. Experimental psychologists, who may have little background in social psychology, will also find this book enjoyable as it highlights a number of social psychological theories succinctly

Do hippocampal pyramidal cells respond to nonspatial stimuli?

There are currently a number of theories of rodent hippocampal function. They fall into two major groups that differ in the role they impute to space in hippocampal information processing. On one hand, the cognitive map theory sees space as crucial and central, with other types of nonspatial information embedded in a primary spatial framework. On the other hand, most other theories see the function of the hippocampal formation as broader, treating all types of information as equivalent and concentrating on the processes carried out irrespective of the specific material being represented, stored, and manipulated. One crucial difference, therefore, is the extent to which theories see hippocampal pyramidal cells as representing nonspatial information independently of a spatial framework. Studies have reported the existence of single hippocampal unit responses to nonspatial stimuli, both to simple sensory inputs as well as to more complex stimuli such as objects, conspecifics, rewards, and time, and these findings been interpreted as evidence in favor of a broader hippocampal function. Alternatively, these nonspatial responses might actually be feature-in-place signals where the spatial nature of the response has been masked by the fact that the objects or features were only presented in one location or one spatial context. In this article, we argue that when tested in multiple locations, the hippocampal response to nonspatial stimuli is almost invariably dependent on the animal’s location. Looked at collectively, the data provide strong support for the cognitive map theory