Spontaneous Breaking of Scale Invariance in a d=3 U(N) Model with Chern-Simons Gauge Field

We study spontaneous breaking of scale invariance in the large N limit of three dimensional $U(N)_\kappa$ Chern-Simons theories coupled to a scalar field in the fundamental representation. When a $\lambda_6(\phi^\dagger\cdot\phi)^3$ self interaction term is added to the action we find a massive phase at a certain critical value for a combination of the $\lambda_6$ and 't Hooft's $\lambda=N/\kappa$ couplings. This model attracted recent attention since at finite $\kappa$ it contains a singlet sector which is conjectured to be dual to Vasiliev's higher spin gravity on $AdS_4$. Our paper concentrates on the massive phase of the 3d boundary theory. We discuss the advantage of introducing masses in the boundary theory through spontaneous breaking of scale invariance.Comment: 23 pages, 8 figures. several lines changed in the introduction. typos correcte

A Hydraulic Approach to Equilibria of Resource Selection Games

Drawing intuition from a (physical) hydraulic system, we present a novel framework, constructively showing the existence of a strong Nash equilibrium in resource selection games (i.e., asymmetric singleton congestion games) with nonatomic players, the coincidence of strong equilibria and Nash equilibria in such games, and the uniqueness of the cost of each given resource across all Nash equilibria. Our proofs allow for explicit calculation of Nash equilibrium and for explicit and direct calculation of the resulting (unique) costs of resources, and do not hinge on any fixed-point theorem, on the Minimax theorem or any equivalent result, on linear programming, or on the existence of a potential (though our analysis does provide powerful insights into the potential, via a natural concrete physical interpretation). A generalization of resource selection games, called resource selection games with I.D.-dependent weighting, is defined, and the results are extended to this family, showing the existence of strong equilibria, and showing that while resource costs are no longer unique across Nash equilibria in games of this family, they are nonetheless unique across all strong Nash equilibria, drawing a novel fundamental connection between group deviation and I.D.-congestion. A natural application of the resulting machinery to a large class of constraint-satisfaction problems is also described.Comment: Hebrew University of Jerusalem Center for the Study of Rationality discussion paper 67

Stable subnorms revisited

Let A be a finite-dimensional, power-associative algebra over a field F, either R or C, and let S, a subset of A, be closed under scalar multiplication. A real-valued function f defined on S, shall be called a subnorm if f(a) > 0 for all 0 not equal a is an element of S, and f(alpha a) = |alpha| f(a) for all a is an element of S and alpha is an element of F. If in addition, S is closed under raising to powers, then a subnorm f shall be called stable if there exists a constant sigma > 0 so that f(a(m)) less than or equal to sigma f(a)(m) for all a is an element of S and m = 1, 2, 3.... The purpose of this paper is to provide an updated account of our study of stable subnorms on subsets of finite-dimensional, power-associative algebras over F. Our goal is to review and extend several of our results in two previous papers, dealing mostly with continuous subnorms on closed sets

Valuation and hedging of the ruin-contingent life annuity (RCLA)

This paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income per year for life, akin to a defined benefit pension, but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters. The motivation for studying the RCLA on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately \$1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. Second, the U.S. administration - both Treasury and Department of Labor - have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job

A Simple Cellular Automation that Solves the Density and Ordering Problems

Cellular automata (CA) are discrete, dynamical systems that perform computations in a distributed fashion on a spatially extended grid. The dynamical behavior of a CA may give rise to emergent computation, referring to the appearance of global information processing capabilities that are not explicitly represented in the system's elementary components nor in their local interconnections.1 As such, CAs o?er an austere yet versatile model for studying natural phenomena, as well as a powerful paradigm for attaining ?ne-grained, massively parallel computation. An example of such emergent computation is to use a CA to determine the global density of bits in an initial state con?guration. This problem, known as density classi?cation, has been studied quite intensively over the past few years. In this short communication we describe two previous versions of the problem along with their CA solutions, and then go on to show that there exists yet a third version | which admits a simple solution