Integrability and chemical potential in the (3+1)-dimensional Skyrme model

Using a remarkable mapping from the original (3+1)dimensional Skyrme model to the Sine-Gordon model, we construct the first analytic examples of Skyrmions as well as of Skyrmions--anti-Skyrmions bound states within a finite box in 3+1 dimensional flat space-time. An analytic upper bound on the number of these Skyrmions--anti-Skyrmions bound states is derived. We compute the critical isospin chemical potential beyond which these Skyrmions cease to exist. With these tools, we also construct topologically protected time-crystals: time-periodic configurations whose time-dependence is protected by their non-trivial winding number. These are striking realizations of the ideas of Shapere and Wilczek. The critical isospin chemical potential for these time-crystals is determined.Comment: 15 pages; 1 figure; a discussion on the closeness to the topological bound as well as some clarifying comments on the semi-classical quantization have been included. Relevant references have been added. Version accepted for publication on Physics Letters

Constraining Monopoles by Topology: an Autonomous System

We find both analytical and numerical solutions of SU(2) Yang-Mills with an adjoint Higgs field within both closed and open tubes whose sections are spherical caps. This geometry admits a smooth limit in which the space-like metric is flat and, moreover, allows one to use analytical tools which in the flat case are not available. Some of the analytic configurations, in the limit of vanishing Higgs coupling, correspond to magnetic monopoles and dyons living within this tube-shaped domain. However, unlike what happens in the standard case, analytical solutions can also be found in the case in which the Higgs coupling is non-vanishing. We further show that the system admits long-lived breathers.Comment: 20 pages, 9 figures, minor corrections, version accepted in JHE

Gauge theories from wrapped and fractional branes

We compare two applications of the gauge/gravity correspondence to a non conformal gauge theory, based respectively on the study of D-branes wrapped on supersymmetric cycles and of fractional D-branes on orbifolds. We study two brane systems whose geometry is dual to N=4, D=2+1 super Yang-Mills theory, the first one describing D4-branes wrapped on a two-sphere inside a Calabi-Yau two-fold and the second one corresponding to a system of fractional D2/D6-branes on the orbifold R^4/Z_2. By probing both geometries we recover the exact perturbative running coupling constant and metric on the moduli space of the gauge theory. We also find a general expression for the running coupling constant of the gauge theory in terms of the "stringy volume" of the two-cycle which is involved in both types of brane systems.Comment: AMS-LaTeX, 35 pages, no figures. Minor typos corrected, version to appear in NP

Analytic crystals of solitons in the four dimensional gauged non-linear sigma model

The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are presented. The complete set of seven coupled non-linear field equations of the gauged non-linear sigma model together with the corresponding Maxwell equations are reduced in a self-consistent way to just one linear Schrodinger-like equation in two dimensions. The corresponding two dimensional periodic potential can be computed explicitly in terms of the solitons profile. The present construction keeps alive the topological charge of the gauged solitons. Both the energy density and the topological charge density are periodic and the positions of their peaks show a crystalline order. These solitons describe configurations in which (most of) the topological charge and total energy are concentrated within three-dimensional tube-shaped regions. The electric and magnetic fields vanish in the center of the tubes and take their maximum values on their surface while the electromagnetic current is contained within these tube-shaped regions. Electromagnetic perturbations of these families of gauged solitons are shortly discussed.Comment: 18 pages, 22 figures, accepted for publication on EUROPEAN PHYSICAL JOURNAL

Analytic Studies of Static and Transport Properties of (Gauged) Skyrmions

We study static and transport properties of Skyrmions living within a finite spatial volume in a flat (3+1)-dimensional spacetime. In particular, we derive an explicit analytic expression for the compression modulus corresponding to these Skyrmions living within a finite box and we show that such expression can produce a reasonable value. The gauged version of these solitons can be also considered. It is possible to analyze the order of magnitude of the contributions to the electrons conductivity associated to the interactions with this Baryonic environment. The typical order of magnitude for these contributions\ to conductivity can be compared with the experimental values of the conductivity of layers of Baryons.Comment: Latex2e source file, 30 pages, 7 figures, accepted for publication in European Physical Journal

Domain wall Skyrmions

Skyrmions of different dimensions are related by domain walls. We obtain explicit full numerical solutions of various Skyrmion configurations trapped inside a domain wall. We find for the quadratic mass-term that multi-Skyrmions are ring-shaped, and conjecture for the linear mass-term, that the lowest-energy state of multi-Skyrmions will consist of charge-2 rings accommodated in a lattice.Comment: LaTeX: 18 pages, 14 figures; V2: typos correcte

Non-extremal fractional branes

We construct non-extremal fractional D-brane solutions of type-II string theory at the Z_2 orbifold point of K3. These solutions generalize known extremal fractional-brane solutions and provide further insights into N=2 supersymmetric gauge theories and dual descriptions thereof. In particular, we find that for these solutions the horizon radius cannot exceed the non-extremal enhancon radius. As a consequence, we conclude that a system of non-extremal fractional branes cannot develop into a black brane. This conclusion is in agreement with known dual descriptions of the system.Comment: 29 pages, LaTeX. v2: 30 pages; equation (3.4) corrected; typos fixed; discussion in section 3 streamlined and slightly extended; reference adde

Transport through Quantum Dots: Analytic Results from Integrability

Recent experiments have probed quantum dots through transport measurements in the regime where they are described by a two lead Anderson model. In this paper we develop a new method to analytically compute for the first time the corresponding transport properties. This is done by using the exact solvability of the Anderson Hamiltonian, together with a generalization of the Landauer-Buttiker approach to integrable systems. The latter requires proper identification of scattering states, a complex and crucial step in our approach. In the Kondo regime, our results include the zero-field, finite temperature linear response conductance, as well as the zero-temperature, non-equilibrium conductance in an applied Zeeman field.Comment: 5 pages, 3 figure