Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories

The theta dependent of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every theta, there are infinitely many vacua that are stable in the large N limit. The true vacuum, found by minimizing the energy in this family, is a smooth function of theta except at theta equal to pi, where it jumps. This jump is associated with spontaneous breaking of CP symmetry. Domain walls separating adjacent vacua are described in terms of wrapped sixbranes.Comment: 8 p

On Induced Gravity in 2-d Topological Theories

We study 2-d $\phi F$ gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals - representing the eigenstates of a vanishing flat potential - are obtained in the $\phi$ representation. The composition of the space they describe is then analyzed: the state corresponding to the singlet representation of the gauge group describes a topological universe. For other representations a metric which is invariant under the residual gauge group is induced, apart from possible topological obstructions. Being inherited from the group metric it is rather rigid.Comment: 38, tex, 160/93/e

Wu-Yang Monopoles and Non-Abelian Seiberg-Witten Equations

Some exact solutions of the SU(2) Seiberg-Witten equations in Minkowski spacetime are given.Comment: 6 pages, LATEX file, no figures. To appear in Mod. Phys. Lett.

Universal Ratios of Characteristic Lengths in Semidilute Polymer Solutions

We use experimental and simulation data from the literature to infer five characteristic lengths, denoted $\xi_s$, $\xi_f$, $\xi_\Pi$, $\xi_\phi$, and $\xi_D$ of a semidilute polymer solution. The first two of these are defined in terms of scattering from the solution, the third is defined in terms of osmotic pressure, the fourth by the spatial monomer concentration profile, and the last by co-operative diffusion. In a given solution the ratios of any of these five lengths are expected to be universal constants. Knowing these constants thus allows one to use one measured property of a solution as a means of inferring others. We calculate these ratios and estimate their uncertainties for solutions in theta as well as good-solvent conditions. The analysis is strengthened by use of scattering properties of isolated polymers inferred from computer simulations.Comment: 15 pages(pdf), to be submitted to Macromolecules or J. Chem. Phy

Making Nuclei Out Of The Skyrme Crystal

A new method for approximating Skyrme solutions is developed. It consists of cutting sections out of the Skyrme crystal and smoothly interpolating between the boundary and spatial infinity. Several field configurations are constructed, and their energies calculated. The surface energy (per unit area) of an infinite flat plane of the crystal is also calculated, and the result used to derive a formula analogous to the semi-empirical mass formula of nuclear physics. This formula can be used to give some idea of what the Skyrme model predicts about volume and surface energies of the nucleus over a broad range of baryon numbers.Comment: 20 pages, uuencoded ps file `crystal.uu'. The LaTeX version can be obtained by emailing [email protected] or [email protected]

The polymer mat: Arrested rebound of a compressed polymer layer

Compression of an adsorbed polymer layer distorts its relaxed structure. Surface force measurements from different laboratories show that the return to this relaxed structure after the compression is released can be slowed to the scale of tens of minutes and that the recovery time grows rapidly with molecular weight. We argue that the arrested state of the free layer before relaxation can be described as a Guiselin brush structure1, in which the surface excess lies at heights of the order of the layer thickness, unlike an adsorbed layer. This brush structure predicts an exponential falloff of the force at large distance with a decay length that varies as the initial compression distance to the 6/5 power. This exponential falloff is consistent with surface force measurements. We propose a relaxation mechanism that accounts for the increase in relaxation time with chain length.Comment: 24 pages, 5 figre