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D. H. Tchrakian

Publications and source records attributed to D. H. Tchrakian.

At least 19 recordsLinked to original sources
arXiv2026

Attractive and repulsive Yang-Mills--Higgs magnetic monopoles on $\mathbb{R}^3$

An $SO(3)$-gauged Higgs model on $\mathbb{R}^3$ is proposed that, like the Abelian Higgs model on $\mathbb{R}^2$, features both attractive and repulsive phases, though unlike the latter its solutions do not saturate the topological lower bound. What distinguishes this model is that its energy is stabilised by the "Higgs analogue of the Chern-Pontryagin" charge, rather than the usual "Higgs--Chern-Pontryagin" charge which is a dimensional descendant of the Chern-Pontryagin charge.

hep-th↗
arXiv2026

Excited solutions in a Skyrme--Chern-Simons model in $2+1$ dimensions

We study excited solutions in a Skyrme--Chern-Simons theory in $2+1$ dimensions. In particular, we emphasize the necessity of using a Lagrange multiplier method to obtain excited solutions, due to the appearance of a discontinuity when using a constraint compliant parametrization. These solutions are characterized by an integer number $p$, excited solutions corresponding to $p\neq 0$. The dependence of the global charges on the parameters is analyzed, showing non-standard behaviors. We also find that the presence of the Skyrme--Chern-Simons term does not alter significantly the pattern of energy levels, so $p=0$ solutions (fundamental solutions) have always the minimal energy.

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arXiv2025

$SO(4)$ gauged $O(5)$ Skyrmion on $\mathbb{R}^4$

We have studied an $SO(4)$ gauged $O(5)$ Skyrmion on $\mathbb{R}^4$ which can be seen as a static soliton in $4+1$ dimensions. This is a sequel of the known $SO(D)$ gauged $O(D+1)$ Skyrmions on $\mathbb{R}^D$ in $D=2$ and in $D=3$, like which they are localised to an absolute scale and are topologically stable, their energies being bounded below by the winding number. In the absence of an analytic proof of existence some such solutions are constructed numerically. Two families of solutions are found, of which only one possesses a gauge decoupling limit. The curvatures of both of these solutions decay as $r^{-3}$, a property they share with the Yang-Mills instantons on $\mathbb{R}^4$.

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arXiv2024

Gauged Skyrme analogue of Chern-Pontryagin

An analogue of the Chern-Pontryagin density for $SO(D)$ gauged $O(D+1)$ Skyrme systems, referred to as Skyrme--Chern-Pontryagin (SCP) densities is known for dimensions $D=2,3,4$. Since these are defined only through a prescription, it is necessary to extend the realisation to higher $D$, which is carried out here for $D=5$. The construction of SCP densities in $D=2,3,4,5$ is presented here in a unified pattern with the aim of pointing out to the possible extrapolation to all dimensions.

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arXiv2024

The effect of Skyrme--Chern-Simons dynamics on gauged Skyrmions in $2+1$ dimensions

We study the Skyrmion of the $SO(2)$ gauged $O(3)$ sigma model in $2+1$ dimensions in the presence of a Skyrme--Chern-Simons (SCS) term, and compare its properties with the corresponding properties of the Skyrmion in the presence of the usual Chern-Simons (CS) term. We find that these properties are qualitatively largely similar in both cases, meaning that the SCS density can be employed as an alternative to the CS term also in higher dimensions, most importantly in even dimensions where no CS term is defined, $e.g.,$ in $3+1$ dimensions. The SCS density employed here is defined in terms of the pair of $SO(2)\times SO(2)$ gauge fields and an auxiliary $O(5)$ Skyrme scalar, which is contracted to an effective $O(3)$ Skyrme scalar. Technically, this study maps the methods to be applied in higher dimensional examples.

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arXiv2023

The role of the Callan-Witten anomaly density as a Chern-Simons term in Skyrme model

We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan-Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy $M$ $vs.$ electric charge $Q_e$ and angular momentum $J$ can be both positive $and$ negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.

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arXiv2022

Some aspects of Skyrme--Chern-Simons densities

The gauge transformation properties of the Skyrme--Chern-Simons (SCS) densities is studied. Two types of SCS actions are identified, Type_{I} in which the gauge group is smaller than the largest possible one, and Type_{II} which are gauged with the largest allowed gauge group. Type_{I} SCS feature only one power of the gauge connection and no curvature, while Type_{II} feature both the gauge connection and the curvature. The Abelian Type_{I} SCS turn out to be explicitly gauge invariant while non-Abelian Type_{I} and all Type_{II} SCS are gauge invariant only up to a total divergence term, and hence lead to gauge covariant equations of motion. SCS actions are the gauged Skyrmion analogues of the usual Chern-Simons (CS) actions, except that unlike the CS which are defined only in odd dimensions, the SCS are defined also in even dimensions. Some areas of application in the construction of solitons are pointed out.

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arXiv2021

Higgs-Chern-Simons gravity models in 2n+1 dimensions

We consider a family of new Higgs-Chern-Simons (HCS) gravity models in 2n+1 dimensions (n=1,2,3). This provides a generalization of the (usual) gravitational Chern-Simons (CS) gravitaties resulting from non- Abelian CS densities in all odd dimensions, which feature vector and scalar fields in addition to the metric. The derivation of the new HCS gravitational (HCSG) actions follows the same method as in the usual-CSG case resulting from the usual CS densities. The HCSG result from the HCS densities, which result through a one-step descent of the Higgs-Chern-Pontryagin (HCP), the latter being descended from Chern-Pontryagin (CP) densities in some even dimension. A preliminary study of the solutions of these models is considered, with exact solutions being reported for spacetime dimensions d = 3, 5.

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arXiv2021

Embedding Gauss-Bonnet scalarization models in higher dimensional topological theories

In the presence of appropriate non-minimal couplings between a scalar field and the curvature squared Gauss-Bonnet (GB) term, compact objects such as neutron stars and black holes (BHs) can spontaneously scalarize, becoming a preferred vacuum. Such strong gravity phase transitions have attracted considerable attention recently. The non-minimal coupling functions that allow this mechanism are, however, always postulated ad hoc. Here we point out that families of such functions naturally emerge in the context of Higgs--Chern-Simons gravity models, which are found as dimensionally descents of higher dimensional, purely topological, Chern-Pontryagin non-Abelian densities. As a proof of concept, we study spherically symmetric scalarized BH solutions in a particular Einstein-GB-scalar field model, whose coupling is obtained from this construction, pointing out novel features and caveats thereof. The possibility of vectorization is also discussed, since this construction also originates vector fields non-minimally coupled to the GB invariant.

gr-qc↗
arXiv2020

On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in $d=4+1$ dimensions

We study an Abelian gauged $O(5)$ Skyrme model in $4+1$ dimensions, featuring the $F^4$ Maxwell and the Chern-Simons terms. Our aim is to expose the mechanism, discovered in the analogous Abelian gauged $O(3)$ Skyrme model in $2+1$ dimensions, which leads to the unusual relation of the mass-energy $E$ to the electric charge $Q_e$ and angular momentum $J$, and, to the change in the value of the "baryon number" $q$ due to the influence of the Abelian field on the Skyrmion. Chern-Simons dynamics together with the dynamics of the gauged Skyrme scalar, allows for solutions with varying asymptotic values of the magnetic field, resulting in these unusual properties listed. Numerical work is carried out on an effective one dimensional subsystem resulting from imposition of an enhaced radial symmetry on ${\mathbb R}^4$.

hep-th↗
arXiv2020

$SO(2)$ gauged Skyrmions in $4+1$ dimensions

We study the simplest $SO(2)$ gauged $O(5)$ Skyrme models in $4+1$ (flat) dimensions. In the gauge decoupled limit, the model supports topologically stable solitons (Skyrmions) and after gauging, the static energy of the solutions is bounded from below by a "baryon number". The studied model features both Maxwell and Maxwell--Chern-Simons dynamics. The considered configurations are subject to bi-azimuthal symmetry in the ${\mathbb R}^4$ subspace resulting in a two dimensional subsystem, as well as subject to an enhanced symmetry relating the two planes in the ${\mathbb R}^4$ subspace, which results in a one dimensional subsystem. Numerical solutions are constructed in both cases. In the purely magnetic case, fully bi-azimuthal solutions were given, while electrically charged and spinning solutions were constructed only in the radial (enhanced symmetric) case, both in the presence of a Chern-Simons term, and in its absence. We find that, in contrast with the analogous models in $2+1$ dimensions, the presence of the Chern-Simons term in the model under study here results only in quantitative effects.

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arXiv2018

Vortices of $SO(2)$ gauged Skyrmions in $2+1$ dimensions

Vortices the $SO(2)$ gauged planar Skyrme model, with a) only Maxwell, b) only Chern-Simons, and c) both Maxwell and Chern-Simons dynamics are studied systematically. In cases a) and b), where both models feature a single parameter $λ$ (the coupling of the potential term), the dependence of the energy on $λ$ is analysed. It is shown that the plots of the energy $vs.$ $λ$ feature discontinuities and branches. In case c), the emphasis is on the evolution of the topological charge, taking non-integer values. Throughout, the properties studied are contrasted with those of the corresponding Abelian Higgs models.

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arXiv2018

On the topological charge of $SO(2)$ gauged Skyrmions in $2+1$ and $3+1$ dimensions

The question of the dependence of the topological charge $q$ of a gauged Skyrmion, on the gauge field, is studied quantitatively. Two examples, both gauged with $SO(2)$ are studied and contrasted: i) The $O(3)$ model in $2+1$ dimensions, and ii) The $O(4)$ model in $3+1$ dimensions. In case i), where the (usual) Chern-Simons (CS) term is present, the value of $q$ changes sign, going through zero. This evolution is tracked by a parameter characterising the solutions in the given theory. In case ii), in which dimensions no CS density is available, the evolution of $q$ is not observed.

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arXiv2018

A Higgs--Chern-Simons gravity model in 2+1 dimensions

We study a gravity model in 2+1 dimensions, arising from a generalized Chern-Simons (CS) density we call a Higgs-Chern-Simons (HCS) density. This generalizes the construction of gravitational systems resulting from non-Abelian CS densities in all odd dimensions. The new HCS densities employed here are arrived at by the usual one-step descent of new Higgs--Chern-Pontryagin (HCP) densities, the latter resulting from the dimensional reduction of Chern-Pontryagin (CP) densities in some even dimension, such that in any given dimension (including even) there is an infinite tower of such models. Here, we restrict our attention to the lowest dimension, 2+1, and to the simplest such model resulting from the dimensional reduction of the $3$-rd CP density. We construct a black hole (BH) solution in closed form, generalizing the familiar BTZ BH. We also study the electrically charged BH solution of the same model augmented with a Maxwell term, and contrast this solution with the electrically charged BTZ BH, specifically concering their respective thermodynamic properties.

gr-qc↗
arXiv2018

Chern-Simons Gravities (CSG) and Gravitational Chern-Simons (GCS) densities in all dimensions

Chern-Simons gravities and gravitational Chern-Simons densities are constructed using the non-Abelian Yang-Mills Chern-Simons densities. As such, they are defined only in odd dimensions. We propose instead an analogous construction employing what we term Higgs--Chern-Simons (HCS) densities, which are defined in $all\ dimensions$. This enables the definition of extended versions of Chern-Simons gravities in all dimensions. Employing the same prescription, the definition of gravitational Chern-Simons densities is extended to all even dimensions, but only to $4p-1$ $odd$ dimensions. All our considerations are restricted to $vacuum$ fields.

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arXiv2017

Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension

We consider a class of generalizations of the Skyrme model to five spacetime dimensions ($d=5$), which is defined in terms of an $O(5)$ sigma model. A special ansatz for the Skyrme field allows angular momentum to be present and equations of motion with a radial dependence only. Using it, we obtain: 1) everywhere regular solutions describing localised energy lumps (Skyrmions); 2) Self-gravitating, asymptotically flat, everywhere non-singular solitonic solutions (Skyrme stars), upon minimally coupling the model to Einstein's gravity; 3) both static and spinning black holes with Skyrme hair, the latter with rotation in two orthogonal planes, with both angular momenta of equal magnitude. In the absence of gravity we present an analytic solution that satisfies a BPS-type bound and explore numerically some of the non-BPS solutions. In the presence of gravity, we contrast the solutions to this model with solutions to a complex scalar field model, namely boson stars and black holes with synchronised hair. Remarkably, even though the two models present key differences, and in particular the Skyrme model allows static hairy black holes, when introducing rotation, the synchronisation condition becomes mandatory, providing further evidence for its generality in obtaining rotating hairy black holes.

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arXiv2017

Reissner-Nordström black holes with non-Abelian hair

We consider $d\geqslant 4$ Einstein--(extended-)Yang-Mills theory, where the gauge sector is augmented by higher order terms. Linearizing the (extended) Yang-Mills equations on the background of the electric Reissner-Nordström (RN) black hole, we show the existence of normalizable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realization of these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged and asymptotically flat black holes with non-Abelian hair. Generically, the hairy black holes are thermodynamically preferred over the RN solution, which, in this model, becomes unstable against the formation of non-Abelian hair, for sufficiently large values of the electric charge.

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