On the relation between effective supersymmetric actions in different dimensions

We make two remarks: (i) Renormalization of the effective charge in a 4--dimensional (supersymmetric) gauge theory is determined by the same graphs and is rigidly connected to the renormalization of the metric on the moduli space of the classical vacua of the corresponding reduced quantum mechanical system. Supersymmetry provides constraints for possible modifications of the metric, and this gives us a simple proof of nonrenormalization theorems for the original 4-dimensional theory. (ii) We establish a nontrivial relationship between the effective (0+1)-dimensional and (1+1)-dimensional Lagrangia (the latter represent conventional Kahlerian sigma models).Comment: 15 pages, 2 figure

Matrix models as solvable glass models

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$ we obtain matrix models and for $p>2$ `tensor' models. We concentrate on the cases $p=2$ which we study analytically and numerically.Comment: 10 pages + 2 figures, Univ.Roma I, 1038/94, ROM2F/94/2

Analysis of Oscillator Neural Networks for Sparsely Coded Phase Patterns

We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical neurodynamics to our model, we theoretically investigate the model's associative memory capability by evaluating its maximum storage capacities and deriving its basins of attraction. It is shown that, as in the Hopfield model, the storage capacity diverges as the activity level decreases. We consider various practically and theoretically important cases. For example, it is revealed that a dynamically adjusted threshold mechanism enhances the retrieval ability of the associative memory. It is also found that, under suitable conditions, the network can recall patterns even in the case that patterns with different activity levels are stored at the same time. In addition, we examine the robustness with respect to damage of the synaptic connections. The validity of these theoretical results is confirmed by reasonable agreement with numerical simulations.Comment: 23 pages, 11 figure

Do Quarks Obey D-Brane Dynamics?

The potential between two D0-branes at rest is calculated to be a linear. Also the potential between two fast decaying D0-branes is found in agreement with phenomenological heavy-quark potentials.Comment: 7 pages, no figures, LaTe

Global structure of exact cosmological solutions in the brane world

We find the explicit coordinate transformation which links two exact cosmological solutions of the brane world which have been recently discovered. This means that both solutions are exactly the same with each other. One of two solutions is described by the motion of a domain wall in the well-known 5-dimensional Schwarzshild-AdS spacetime. Hence, we can easily understand the region covered by the coordinate used by another solution.Comment: Latex, 9 pages including 5 figures; references add, accepted for publication in Physical Review

Solutions to the cosmological constant problems

We critically review several recent approaches to solving the two cosmological constant problems. The "old" problem is the discrepancy between the observed value of $\Lambda$ and the large values suggested by particle physics models. The second problem is the "time coincidence" between the epoch of galaxy formation $t_G$ and the epoch of $\Lambda$-domination t_\L. It is conceivable that the "old" problem can be resolved by fundamental physics alone, but we argue that in order to explain the "time coincidence" we must account for anthropic selection effects. Our main focus here is on the discrete-$\Lambda$ models in which $\Lambda$ can change through nucleation of branes. We consider the cosmology of this type of models in the context of inflation and discuss the observational constraints on the model parameters. The issue of multiple brane nucleation raised by Feng {\it et. al.} is discussed in some detail. We also review continuous-\L models in which the role of the cosmological constant is played by a slowly varying potential of a scalar field. We find that both continuous and discrete models can in principle solve both cosmological constant problems, although the required values of the parameters do not appear very natural. M-theory-motivated brane models, in which the brane tension is determined by the brane coupling to the four-form field, do not seem to be viable, except perhaps in a very tight corner of the parameter space. Finally, we point out that the time coincidence can also be explained in models where $\Lambda$ is fixed, but the primordial density contrast $Q=\delta\rho/\rho$ is treated as a random variable.Comment: 30 pages, 3 figures, two notes adde