Dynamical SUSY and R-symmetry breaking in SQCD with massive and massless flavors

We show that supersymmetry and R-symmetry can be dynamically broken in a long-lived metastable vacuum of SQCD with massive and massless flavors. The vacuum results from a competition of a (leading) two-loop effect and small "Planck" suppressed higher-dimension operators. This mechanism provides a particularly simple realization of dynamical SUSY and R-symmetry breaking, and as such it is a good starting point for building phenomenologically viable models of gauge mediation. We take a preliminary step in this direction by constructing a complete model of minimal gauge mediation. Here we find that the parameters of the model are surprisingly constrained by the hidden sector. Similar mechanisms for creating long-lived states operate in a large class of models.Comment: 25 pages. v2: added references, minor correctio

Field-Theoretic Simulations of Polyelectrolyte Complexation

We briefly discuss our recent field-theoretic study of polyelectrolyte complexation, which occurs in solutions of two oppositely charged polyelectrolytes. Charged systems require theoretical methods beyond the mean-field (or self-consistent field) approximation; indeed, mean-field theory is qualitatively incorrect for such polyelectrolyte solutions. Both analytical (one-loop) and numerical (complex Langevin) methods to account for charge correlations are discussed. In particular, the first application of field-theoretic simulations to polyelectrolyte systems is reported. The polyelectrolyte charge-charge correlation length and a phase diagram are provided; effects of charge redistribution are qualitatively explored.Comment: 7 pages, 3 figures, 3 equations, LaTeX; accepted to Journal of Polymer Science B: Polymer Physics; v2: a revised and expanded version, 6 paragraphs of text and about 20 references adde

Scaling relations between numerical simulations and physical systems they represent

The dynamical equations describing the evolution of a physical system generally have a freedom in the choice of units, where different choices correspond to different physical systems that are described by the same equations. Since there are three basic physical units, of mass, length and time, there are up to three free parameters in such a rescaling of the units, $N_f \leq 3$. In Newtonian hydrodynamics, e.g., there are indeed usually three free parameters, $N_f = 3$. If, however, the dynamical equations contain a universal dimensional constant, such as the speed of light in vacuum $c$ or the gravitational constant $G$, then the requirement that its value remains the same imposes a constraint on the rescaling, which reduces its number of free parameters by one, to $N_f = 2$. This is the case, for example, in magneto-hydrodynamics (MHD) or special relativistic hydrodynamics, where $c$ appears in the dynamical equations and forces the length and time units to scale by the same factor, or in Newtonian gravity where the gravitational constant $G$ appears in the equations. More generally, when there are $N_{udc}$ independent (in terms of their units) universal dimensional constants, then the number of free parameters is $N_f = max(0,3-N_{udc})$. When both gravity and relativity are included, there is only one free parameter ($N_f = 1$, as both $G$ and $c$ appear in the equations so that $N_{udc} = 2$), and the units of mass, length and time must all scale by the same factor. The explicit rescalings for different types of systems are discussed and summarized here. Such rescalings of the units also hold for discrete particles, e.g. in N-body or particle in cell simulations. They are very useful when numerically investigating a large parameter space or when attempting to fit particular experimental results, by significantly reducing the required number of simulations.Comment: 6 pages, 2 tables, accepted to MNRAS (expanded discussion of the general context in the introduction

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

The importance of quantum decoherence in brain processes

Based on a calculation of neural decoherence rates, we argue that that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence timescales ~10^{-13}-10^{-20} seconds are typically much shorter than the relevant dynamical timescales (~0.001-0.1 seconds), both for regular neuron firing and for kink-like polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.Comment: Minor changes to match accepted PRE version. 15 pages with 5 figs included. Color figures and links at http://www.physics.upenn.edu/~max/brain.html or from [email protected]. Physical Review E, in pres

Entrepreneurs’ age, institutions, and social value creation goals: a multi-country study

This study explores the relationship between an entrepreneur's age and his/her social value creation goals. Building on the lifespan developmental psychology literature and institutional theory, we hypothesize a U-shaped relationship between entrepreneurs’ age and their choice to create social value through their ventures, such that younger and older entrepreneurs create more social value with their businesses while middle age entrepreneurs are relatively more economically and less socially oriented with their ventures. We further hypothesize that the quality of a country’s formal institutions in terms of economic, social, and political freedom steepen the U-shaped relationship between entrepreneurs’ age and their choice to pursue social value creation as supportive institutional environments allow entrepreneurs to follow their age-based preferences. We confirm our predictions using multilevel mixed-effects linear regressions on a sample of over 15,000 entrepreneurs (aged between 18 and 64 years) in 45 countries from Global Entrepreneurship Monitor data. The findings are robust to several alternative specifications. Based on our findings, we discuss implications for theory and practice, and we propose future research directions

Uplifted Metastable Vacua and Gauge Mediation in SQCD

Anomalously small gaugino masses are a common feature of various models of direct gauge mediation. This problem is closely related to the vacuum structure of the theory. In this paper we show that massive SQCD can have SUSY-breaking vacua which are qualitatively different from the ISS vacuum. These novel vacua are metastable with respect to decay to the ISS vacuum. We demonstrate the possibility of addressing the gaugino mass problem in this framework. We study the properties of these vacua and construct an example of a model of direct gauge mediation.Comment: Latex, 23 page

What Makes Entrepreneurs Happy? Determinants of Satisfaction Among Founders

This study empirically investigates factors influencing satisfaction levels of founders of new ventures, using a representative sample of 1,107 Dutch founders. We relate entrepreneurial satisfaction (with income, psychological burden and leisure time) to firm performance, motivation and human capital. Founders with high levels of specific human capital are more satisfied with income than those with high levels of general human capital. Intrinsic motivation and that of combining responsibilities lowers stress and leads to more satisfaction with leisure time. Women are more satisfied with their income than men, even though they have a lower average monthly turnover