A Note on Chern-Simons Solitons - a type III vortex from the wall vortex

We study some properties of topological Chern-Simons vortices in 2 + 1 dimensions. As has already been understood in the past, in the large magnetic flux limit, they are well described by a Chern-Simons domain wall, which has been compactified on a circle with the symmetric phase inside and the asymmetric phase on the outside. Our goal is two-fold. First we want to explore how the tension depends on the magnetic flux discretized by the integer n. The BPS case is already known, but not much has been explored about the non-BPS potentials. A generic renormalizable potential has two dimensionless parameters that can be varied. Variation of only one of them lead to a type I and type II vortex, very similar to the Abrikosov-Nielsen-Olesen (ANO) case. Variation of both the parameters leads to a much richer structure. In particular we have found a new type of vortex, which is type I-like for small flux and then turns type II-like for larger flux. We could tentatively denote it a type III vortex. This results in a stable vortex with number of fluxes which can be greater than one. Our second objective is to study the Maxwell-Chern-Simons theory and and understand how the large n limit of the CS vortex is smoothly connected with the large n limit of the ANO vortex.Comment: 27 pages, 17 figures; v2.: references added, subsection 3.2 added, explanation added in section 2.

Magnetic Bags and Black Holes

We discuss gravitational magnetic bags, i.e. clusters of large number of monopoles in presence of gravitational effects. Physics depends on the dimensionless ratio between the vev of the Higgs field at infinity and the Planck mass. We solve the equations for the gravitational bags, and study the transition from monopole to black hole. The critical coupling for this transition is $v_{cr} = \sqrt{\pi}/(4 \sqrt{G})$, and it is larger than that of a single 't Hooft-Polyakov monopole. We investigate in detail the black-hole limit.Comment: 20 pages, 12 figures; v2 small change

Skyrmions in Orientifold and Adjoint QCD

This is a review of recent developments regarding the Skyrmion sector of higher representation QCD. Ordinary QCD is a SU(n) gauge theory with n_f Dirac quarks in the fundamental representation. Changing the representation of quarks leads to different and interesting theories, which are not as well studied as ordinary QCD. In order to be able to have a consistent asymptotically free large n limit, we must limit ourselves to three cases: two-index representation (symmetric or anti-symmetric) and adjoint representation. Skyrmions of the low-energy effective Lagrangian shall be the main subject of this review. There are puzzling aspects, both in orientifold and adjoint QCD, regarding the identification of the Skyrmion and its quantum stability, that have not yet been understood. We shall explain these problems and the solution we proposed for them. The first part is dedicated to the two-index representation. Here the challenge is to identify the correct particle in the spectrum that has to be identified with the Skyrmion. It turns out not to be the simplest baryon (as in ordinary QCD) but a baryonic state with higher charge, precisely composed by n(n\pm 1)/2 quarks. Although not the simplest among the baryons, it is the one that minimizes the mass per unit of baryonic charge and thus is the most stable among them. The second part is devoted to the quarks in the adjoint representation. The task here assume a different perspective. We do not have a baryon charge, like in ordinary QCD. An important role is now played by a massive fermion that must be considered in the low-energy effective Lagrangian. Through this fermion, the Skyrmion acquires an anomalous fermionic number (-1)^F and, as a consequence, an odd relationship between the latter and its spin/statistic. This implies a Z_2 stability of the Skyrmion.Comment: 38 pages; 15 figures. v2: ref adde

Born Reciprocity and Cosmic Accelerations

The trans-Planckian theory is a model that realizes concretely the Born reciprocity idea, which is the postulate of absolute equivalence between coordinate $x$ and momenta $p$. This model is intrinsically global, and thus it is naturally implemented in a cosmological setting. Cosmology and Born reciprocity are made for each other. Inflation provides the essential mechanism to suppress the terms coming from the dual part of the action. The trans-Planckian theory provides an explanation for the present acceleration of the universe scale factor. This is possible just considering a simple model that contains gravity, one gauge field plus one matter field (to be identified with dark matter), together with the reciprocity principle.Comment: 22 pages, 5 figures. v2: minor corrections. v3: book chapter of "Advances in Dark Energy Research". v4: some correction

Forgetful linear systems on the projective space and rational normal curves over \cM_{0,2n}^{GIT}

Let \cM_{0,n} the moduli space of $n$-pointed rational curves. The aim of this note is to give a new, geometric construction of \cM_{0,2n}^{GIT}, the GIT compacification of \cM_{0,2n}, in terms of linear systems on \PP^{2n-2} that contract all the rational normal curves passing by the points of a projective base. These linear systems are a projective analogue of the forgetful maps between \bar{\cM}_{0,2n+1} and \bar{\cM}_{0,2n}. The construction is performed via a study of the so-called $\textit{contraction}$ maps from the Knudsen-Mumford compactification \bar{\cM}_{0,2n} to \cM_{0,2n}^{GIT} and of the canonical forgetful maps. As a side result we also find a linear system on \bar{\cM}_{0,2n} whose associated map is the contraction map $c_{2n}$.Comment: New version: corrected typos, added contextualization and relations with previous GIT constructions and with linear systems on the Knudsen compactificatio

Instanton Bags, High Density Holographic QCD and Chiral Symmetry Restoration

We describe the simplest example of an instanton bag in Euclidean space. It consists of a monopole wall and a Kaluza-Klein monopole wall, lifted to one higher dimension, trapping the instanton charge in the middle. This object has finite instanton density in a three-dimensional volume. Baryon physics in holographic QCD models gets translated into a multi-instanton problem in the bulk, and a state with a high density baryonic charge consists of a non-diluted multi-instanton solution. The instanton bag is a good candidate for this high-density state. We compute its parameters via moduli stabilization. Chiral symmetry restoration is exhibited by this state, and it is a direct consequence of its non-diluted features.Comment: 32 pages, 11 figures; v2: revised version, accepted on pr

A conic bundle degenerating on the Kummer surface

Let $C$ be a genus 2 curve and \su the moduli space of semi-stable rank 2 vector bundles on $C$ with trivial determinant. In \cite{bol:wed} we described the parameter space of non stable extension classes (invariant with respect to the hyperelliptic involution) of the canonical sheaf $\omega$ of $C$ with $\omega_C^{-1}$. In this paper we study the classifying rational map \phi: \pr Ext^1(\omega,\omega^{-1})\cong \pr^4 \dashrightarrow \su\cong \pr^3 that sends an extension class on the corresponding rank two vector bundle. Moreover we prove that, if we blow up \pr^4 along a certain cubic surface $S$ and \su at the point $p$ corresponding to the bundle \OO \oplus \OO, then the induced morphism \tilde{\phi}: Bl_S \ra Bl_p\su defines a conic bundle that degenerates on the blow up (at $p$) of the Kummer surface naturally contained in \su. Furthermore we construct the \pr^2-bundle that contains the conic bundle and we discuss the stability and deformations of one of its components.Comment: 29 page

W/Z and diboson production at hadron colliders

A general review of the latest results about single and double vector boson production in the multipurpose experiments at LHC (ATLAS and CMS) and at Tevatron (CDF and D0) will be presented. The review will focus on boson production, while a more detailed report about W and Z properties can be found elsewhere. Only leptonic decays into electrons and muons will be considered.Comment: 7 pages, 6 figures, proceedings of XXXI PHYSICS IN COLLISION, Vancouver, BC Canada, August 28 - September 1, 201