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

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

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

Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions

We study the baby Skyrme model as a theory that interpolates between two distinct BPS systems. For this a near-BPS approximation can be used which, however, involves a small deviation from each of the two BPS limits. We provide analytical explanation and numerical support for the validity of this approximation. We then study the set of all possible supersymmetric extensions of the baby Skyrme model with ${\cal N}=1$ and the particular ones with extended ${\cal N}=2$ supersymmetries and relate this to the above mentioned almost-BPS approximation.Comment: 23 pages, 5 figures, v2: explanations adde

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.

Comments on Critical Electric and Magnetic Fields from Holography

We discuss some aspects of critical electric and magnetic fields in a field theory with holographic dual description. We extend the analysis of arxiv:1109.2920, which finds a critical electric field at which the Schwinger pair production barrier drops to zero, to the case of magnetic fields. We first find that, unlike ordinary weakly coupled theories, the magnetic field is not subject to any perturbative instability originating from the presence of a tachyonic ground state in the W-boson spectrum. This follows from the large value of the 't Hooft coupling \lambda, which prevents the Zeeman interaction term to overcome the particle mass at high B. Consequently, we study the next possible B-field instability, i.e. monopole pair production, which is the S-dual version of the Schwinger effect. Also in this case a critical magnetic field is expected when the tunneling barrier drops to zero. These Schwinger-type criticalities are the holographic duals, in the bulk, to the fields E or B reaching the tension of F1 or D1 strings respectively. We then discuss how this effect is modified when electric and magnetic fields are present simultaneously and dyonic states in the spectrum can be pair produced by a generic E - B background. Finally, we analyze finite temperature effects on Schwinger criticalities, i.e. in the AdS-Schwarzshild black hole background.Comment: 33 pages, 4 figures; v2: refs added; v3: typos corrected, to appear on JHE

Higher Winding Strings and Confined Monopoles in N=2 SQCD

We consider composite string solutions in N=2 SQCD with the gauge group U(N), the Fayet--Iliopoulos term \xi \neq 0 and N (s)quark flavors. These bulk theories support non-Abelian strings and confined monopoles identified with kinks in the two-dimensional world-sheet theory. Similar and more complicated kinks (corresponding to composite confined monopoles) must exist in the world-sheet theories on composite strings. In a bid to detect them we analyze the Hanany--Tong (HT) model, focusing on a particular example of N=2. Unequal quark mass terms in the bulk theory result in the twisted masses in the N=(2,2) HT model. For spatially coinciding 2-strings, we find three distinct minima of potential energy, corresponding to three different 2-strings. Then we find BPS-saturated kinks interpolating between each pair of vacua. Two kinks can be called elementary. They emanate one unit of the magnetic flux and have the same mass as the conventional 't Hooft--Polyakov monopole on the Coulomb branch of the bulk theory (\xi =0). The third kink represents a composite bimonopole, with twice the minimal magnetic flux. Its mass is twice the mass of the elementary confined monopole. We find instantons in the HT model, and discuss quantum effects in composite strings at strong coupling. In addition, we study the renormalization group flow in this model.Comment: 41 pages, 11 figure

Quantum Fusion of Domain Walls with Fluxes

We study how fluxes on the domain wall world volume modify quantum fusion of two distant parallel domain walls into a composite wall. The elementary wall fluxes can be separated into parallel and antiparallel components. The parallel component affects neither the binding energy nor the process of quantum merger. The antiparallel fluxes, instead, increase the binding energy and, against naive expectations, suppress quantum fusion. In the small flux limit we explicitly find the bounce solution and the fusion rate as a function of the flux. We argue that at large (antiparallel) fluxes there exists a critical value of the flux (versus the difference in the wall tensions), which switches off quantum fusion altogether. This phenomenon of flux-related wall stabilization is rather peculiar: it is unrelated to any conserved quantity. Our consideration of the flux-related all stabilization is based on substantiated arguments that fall short of complete proof.Comment: 17 pages, 3 figure

The Skyrmion strikes back: baryons and a new large NcN_c limit

In the large $N_c$ limit of QCD, baryons can be modeled as solitons, for instance, as Skyrmions. This modeling has been justified by Witten's demonstration that all properties of baryons and mesons scale with $N_c^{-1/2}$ in the same way as the analogous meson-based soliton model scales with a generic meson-meson coupling constant $g$. An alternative large $N_c$ limit (the orientifold large $N_c$ limit) has recently been proposed in which quarks transform in the two-index antisymmetric representation of $SU(N_c)$. By carrying out the analog of Witten's analysis for the new orientifold large $N_c$ limit, we show that baryons and solitons can also be identified in the orientifold large $N_c$ limit. However, in the orientifold large $N_c$ limit, the interaction amplitudes and matrix elements scale with $N_c^{-1}$ in the same way as soliton models scale with the generic meson coupling constant $g$ rather than as $N_c^{-1/2}$ as in the traditional large $N_c$ limit.Comment: 10 pages, 26 figure

Confinement and Localization on Domain Walls

We continue the studies of localization of the U(1) gauge fields on domain walls. Depending on dynamics of the bulk theory the gauge field localized on the domain wall can be either in the Coulomb phase or squeezed into flux tubes implying (Abelian) confinement of probe charges on the wall along the wall surface. First, we consider a simple toy model with one flavor in the bulk at weak coupling (a minimal model) realizing the latter scenario. We then suggest a model presenting an extension of the Seiberg--Witten theory which is at strong coupling, but all theoretical constructions are under full control if we base our analysis on a dual effective action. Finally, we compare our findings with the wall in a "nonminimal" theory with two distinct quark flavors that had been studied previously. In this case the U(1) gauge field trapped on the wall is exactly massless because it is the Goldstone boson of a U(1) symmetry in the bulk spontaneously broken on the wall. The theory on the wall is in the Coulomb phase. We explain why the mechanism of confinement discussed in the first part of the paper does not work in this case, and strings are not formed on the walls.Comment: 55 pp; v2: several remarks adde