arXiv subjects

C. P. Constantinidis

Publications and source records attributed to C. P. Constantinidis.

At least 19 recordsLinked to original sources

arXiv2026

New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations

Positive and negative flows of the Chen-Lee-Liu model and its various reductions, including Burgers hierarchy, are formulated within the framework of Riemann-Hilbert-Birkhoff decomposition with the constant grade two generator. Two classes of vacua, namely zero vacuum and constant non-zero vacuum can be realized within a centerless Heisenberg algebra. The tau functions for soliton solutions are obtained by a dressing method and vertex operators are constructed for both types of vacua. We are able to select and classify the soliton solutions in terms of the type of vertices involved. A judicious choice of vertices yields in a closed form a particular set of multi soliton solutions for the Burgers hierarchy. We develop and analyze a class of gauge-Bäcklund transformations that generate further multi soliton solutions from those obtained by dressing method by letting them interact with various integrable defects.

nlin.SI↗

arXiv2025

Generalized Riemann-Hilbert-Birkhoff Decomposition and a New Class of Higher Grading Integrable Hierarchies

We propose a generalized Riemann-Hilbert-Birkhoff decomposition that expands the standard integrable hierarchy formalism in two fundamental ways: it allows for integer powers of Lax matrix components in the flow equations to be increased as compared to conventional models, and it incorporates constant non-zero vacuum (background) solutions. Two additional parameters control these features. The first one defines the grade of a semisimple element that underpins the algebraic construction of the hierarchy, where a grade-one semi-simple element recovers known hierarchies such as mKdV and AKNS. The second parameter distinguishes between zero and non-zero constant background (vacuum) configurations. Additionally, we introduce a third parameter associated with an ambiguity in the definition of the grade-zero component of the dressing matrices. While not affecting the decomposition itself, this parameter classifies different gauge realizations of the integrable equations (like for example, Kaup-Newell, Gerdjikov-Ivanov, Chen-Lee-Liu models). For various values of these parameters, we construct and analyze corresponding integrable models in a unified universal manner demonstrating the broad applicability and generative power of the extended formalism.

nlin.SI↗

arXiv2019

A mild source for the Wu-Yang magnetic monopole

We establish that the Wu-Yang monopole needs the introduction of a magnetic point source at the origin in order for it to be a solution of the differential and integral equations for the Yang-Mills theory. That result is corroborated by the analysis through distribution theory, of the two types of magnetic fields relevant for the local and global properties of the Wu-Yang solution. The subtlety lies on the fact that with the non-vanishing magnetic point source required by the Yang-Mills integral equations, the Wu-Yang monopole configuration does not violate, in the sense of distribution theory, the differential Bianchi identity.

hep-th↗

arXiv2017

A direct test of the integral Yang-Mills equations through SU(2) monopoles

We use the SU(2) 't Hooft-Polyakov monopole configuration, and its BPS version, to test the integral equations of the Yang-Mills theory. Those integral equations involve two (complex) parameters which do not appear in the differential Yang-Mills equations, and if they are considered to be arbitrary it then implies that non-abelian gauge theories (but not abelian ones) possess an infinity of integral equations. For static monopole configurations only one of those parameters is relevant. We expand the integral Yang-Mills equation in a power series of that parameter and show that the 't Hooft-Polyakov monopole and its BPS version satisfy the integral equations obtained in first and second order of that expansion. Our results points to the importance of exploring the physical consequences of such an infinity of integral equations on the global properties of the Yang-Mills theory.

hep-th↗

arXiv2015

A remark on the asymptotic form of BPS multi-dyon solutions and their conserved charges

We evaluate the gauge invariant, dynamically conserved charges, recently obtained from the integral form of the Yang-Mills equations, for the BPS multi-dyon solutions of a Yang-Mills-Higgs theory associated to any compact semi-simple gauge group G. Those charges are shown to correspond to the eigenvalues of the next-to-leading term of the asymptotic form of the Higgs field at spatial infinity, and so coinciding with the usual topological charges of those solutions. Such results show that many of the topological charges considered in the literature are in fact dynamical charges, which conservation follows from the global properties of classical Yang-Mills theories encoded into their integral dynamical equations. The conservation of those charges can not be obtained from the differential form of Yang-Mills equations.

hep-th↗

arXiv2013

New Massive Gravity Holography

We investigate the holographic renormalization group flows and the classical phase transitions that occur in two dimensional QFT model dual to the New Massive 3D Gravity coupled to scalar matter. Specific matter self-interactions generated by quadratic superpotential are considered. The off-critical $AdS_3/CFT_2$ correspondence determines the exact form of the $ QFT_2$ 's $β$ -function and the singular part of the reduced free energy. The corresponding scaling laws and critical exponents characterizing the RG fixed points as well as the values of the mass gaps in the massive phases are obtained.

hep-th↗

arXiv2013

Self-Duality from New Massive Gravity Holography

The holographic renormalization group (RG) flows in certain self-dual two dimensional QFT's models are studied. They are constructed as holographic duals to specific New Massive 3d Gravity (NMG) models coupled to scalar matter with "partially self-dual" superpotentials. The standard holographic RG constructions allow us to derive the exact form of their $β$- functions in terms of the corresponding NMG's domain walls solutions. By imposing invariance of the free energy, the central function and of the anomalous dimensions under specific matter field's duality transformation, we have found the conditions on the superpotentials of two different NMG's models, such that their dual 2d QFT's are related by a simple strong-weak coupling transformation.

hep-th↗

arXiv2012

Domain Walls in Extended Lovelock Gravity

We derive a BPS-like first order system of equations for a family of flat static domain walls (DWs) of dimensionally extended cubic Lovelock Gravity coupled to massive scalar self-interacting matter. The explicit construction of such DWs is achieved by introducing of an appropriate matter superpotential. We further analyse the dependence of the geometric properties of the asymptotically AdSd space-times representing distinct DWs on the shape of the matter potential, on the values of the Lovelock couplings and on the scalar field boundary conditions. Few explicit examples of Lovelock DWs interpolating between AdS-type vacua of different cosmological constants are presented. In five dimensions our method provides interesting solutions of the Myers-Robinson Quasi-topological Gravity in the presence of matter important for the description of the specific renormalization group flows in its holographic dual four-dimensional CFT perturbed by relevant operators.

hep-th↗

arXiv2005

Falsifying Tree Level String Motivated Bouncing Cosmologies

The string effective action at tree level contains, in its bosonic sector, the Einstein-Hilbert term, the dilaton, and the axion, besides scalar and gauge fields coming from the Ramond-Ramond sector. The reduction to four dimensions brings to scene moduli fields. We generalize this effective action by introducing two arbitrary parameters, $ω$ and $m$, connected with the dilaton and axion couplings. In this way, more general frameworks can be analyzed. Regular solutions with a bounce can be obtained for a range of (negative) values of the parameter $ω$ which, however, exclude the pure string configuration ($ω= - 1$). We study the evolution of scalar perturbations in such cosmological scenarios. The predicted primordial power spectrum decreases with the wavenumber with spectral index $n_s=-2$, in contradiction with the results of the $WMAP$. Hence, all such effective string motivated cosmological bouncing models seem to be ruled out, at least at the tree level approximation.

hep-th↗

arXiv2004

Symmetries and observables in topological gravity

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.

gr-qc↗

arXiv2004

Observables in Topological Theories: A Superspace Formulation

Observables of topological Yang-Mills theory were defined by Witten as the classes of an equivariant cohomology. We propose to define them alternatively as the BRST cohomology classes of a superspace version of the theory, where BRST invariance is associated to super Yang-Mills invariance. We provide and discuss the general solution of this cohomology.

hep-th↗

arXiv2003

A gauge invariant formulation for the SU(N) non-linear sigma model in 2+1 dimensions

We derive a local, gauge invariant action for the SU(N) non-linear sigma-model in 2+1 dimensions. In this setting, the model is defined in terms of a self-interacting pseudo vector-field θ_μ, with values in the Lie algebra of the group SU(N). Thanks to a non-trivially realized gauge invariance, the model has the correct number of degrees of freedom: only one polarization of θ_μ, like in the case of the familiar Yang-Mills theory in 2+1 dimensions. Moreover, since θ_μis a pseudo-vector, the physical content corresponds to one massless pseudo-scalar field in the Lie algebra of SU(N), as in the standard representation of the model. We show that the dynamics of the physical polarization corresponds to that of the SU(N) non-linear sigma model in the standard representation, and also construct the corresponding BRST invariant gauge-fixed action.

hep-th↗

arXiv2002

Construction of exact Riemannian instanton solutions

We give the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2d Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta function source. Using techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

hep-th↗

arXiv2001

On the symmetries of BF models and their relation with gravity

The perturbative finiteness of various topological models (e.g. BF models) has its origin in an extra symmetry of the gauge-fixed action, the so-called vector supersymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we first extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the Batalin-Vilkovisky framework. Thereafter, we address the relationship between gravity and BF models, in particular for three-dimensional space-time.

hep-th↗

arXiv2000

Regularity and stability of electrostatic solutions in Kaluza-Klein theory

We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Besides black holes and wormholes, a new class of geodesically complete solutions is identified. A monopole perturbation is carried out, enabling us to prove analytically the stability of a large class of solutions, including all black holes and neutral solutions.

gr-qc↗

arXiv1999

A solution to the zero-hamiltonian problem in 2-D gravity

The zero-hamiltonian problem, present in reparametrization invariant systems, is solved for the 2-D induced gravity model. Working with methods developed by Henneaux et al. we find systematically the reduced phase-space physics, generated by an {\it effective} hamiltonian obtained after complete gauge fixing.

hep-th↗

arXiv1999

Electrostatic solutions in Kaluza-Klein theory: geometry and stability

We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Both charged and neutral cases are considered. The analysis of the solutions, through their geometrical properties, reveals the existence of black holes, wormholes and naked singularities. A new class of regular solutions is identified. A monopole perturbation study of all these solutions is carried out, enabling us to prove analytically the stability of large classes of solutions. In particular, the black hole solutions are stable, while for the regular solutions the stability analysis leads to an eigenvalue problem.

gr-qc↗

arXiv1999

Regular Bouncing Cosmological Solutions in Effective Actions in Four Dimensions

We study cosmological scenarios resulting from effective actions in four dimensions which are, under some assumptions, connected with multidimensional, supergravity and string theories. These effective actions are labeled by the parameters $ω$, the dilaton coupling constant, and $n$ which establishes the coupling between the dilaton and a scalar field originated from the gauge field existing in the original theories. There is a large class of bouncing as well as Friedmann-like solutions. We investigate under which conditions bouncing regular solutions can be obtained. In the case of the string effective action, regularity is obtained through the inclusion of contributions from the Ramond-Ramond sector of superstring.

gr-qc↗