Searcharxiv⌕ Search

arXiv subjects

Ctirad Klimcik

Publications and source records attributed to Ctirad Klimcik.

At least 19 recordsLinked to original sources
arXiv2026

Euclidean E-models

We develop the theory of the first-order dynamical systems, called the Euclidean $\mathcal E$-models, which naturally give rise in their second-order formulation to non-unitary nonlinear $σ$-models with real Euclidean actions. We establish the Euclidean version of Poisson--Lie T-duality, formulate sufficient conditions for Lax integrability, and describe the one-loop renormalization flow of the Euclidean $\mathcal E$-operator. For perfect Drinfeld doubles, we introduce the $\mathcal E$-Wick rotation, which canonically associates a Euclidean $\mathcal E$-model with every Lorentzian one. In the families studied here, this construction induces natural analytic continuations relating the Lorentzian and Euclidean Lax representations and renormalization-group flows, while preserving Poisson--Lie duality. As the principal example, we construct the Euclidean bi-Yang--Baxter model on the Lu--Weinstein double and determine explicitly its action, Lax representation, Poisson--Lie dual and one-loop renormalization-group flow. We identify a one-parameter family of one-loop RG fixed points for which the target-space geometry develops singularities on the maximal torus of $K$, whereas the dual model with target $K^{\mathbb C}/K$ has an everywhere regular background. This regular dual model turns out to be a one-parameter deformation of the non-unitary hyperbolic Wess--Zumino--Witten model.

hep-th↗
arXiv2024

On integrable deformations of the Cherednik model

We provide the E-model formulation of the non-deformed Cherednik model as well as of its Poisson-Lie and Poisson-Lie-WZ deformed version. In all three cases we solve the sufficient condition of integrability by using the E-model formalism. We thus recover in an alternative way the known results for the non-deformed and the Poisson-Lie deformed models, while for the Poisson-Lie-WZ deformed one our results are new.

hep-th↗
arXiv2023

Point particle E-models

We show that the same algebraic data that permit to construct the Lax pair and the $r$-matrix of an integrable non-linear $σ$-model in $1+1$ dimensions can be also used for the construction of Lax pairs and of $r$-matrices of several other non-trivial integrable theories in $1+0$ dimension. We call those new integrable theories the point particle ${\cal E}$-models, we describe their structure and give their physical interpretation. We work out in detail the point particle ${\cal E}$-models associated to the bi-Yang-Baxter deformation of the $SU(N)$ principal chiral model. In particular, for each complex flag manifold we thus obtain a two-parameter family of integrable models living on it.

math-ph↗
arXiv2022

Superintegrability, symmetry and point particle T-duality

We show that the ideas related to integrability and symmetry play an important role not only in the string T-duality story but also in its point particle counterpart. Applying those ideas, we find that the T-duality seems to be a more widespread phenomenon in the context of the point particle dynamics than it is in the string one; moreover, it concerns physically very relevant point particle dynamical systems and not just somewhat exotic ones fabricated for the purpose. As a source of T-duality examples, we consider maximally superintegrable spherically symmetric electro-gravitational backgrounds in $n$ dimensions. We then describe in detail four such spherically symmetric dynamical systems which are all mutually interconnected by a web of point particle T-dualities. In particular, the dynamics of a charged particle scattered by a repulsive Coulomb potential in a flat space is T-dual to the dynamics of the Coulomb scattering in the space of constant negative curvature, but it is also T-dual to the (conformal) Calogero-Moser inverse square dynamics both in flat and hyperbolic spaces. Thus knowing just the Hamiltonian dynamics of the scattered particle cannot give us an information about the curvature of the space in which the particle moves.

hep-th↗
arXiv2021

On strong integrability of the dressing cosets

We formulate sufficient conditions for the strong integrability of dressing cosets. We provide several sigma-model backgrounds solving those conditions, some of them are new and some of them were not so far formulated as the dressing cosets. The new models are based on the Drinfeld doubles having the structure of higher order jet bundles of quadratic Lie groups.

hep-th↗
arXiv2021

Brief lectures on duality, integrability and deformations

We provide a pedagogical introduction to some aspects of integrability, dualities and deformations of physical systems in 0+1 and in 1+1 dimensions. In particular, we concentrate on the T-duality of point particles and strings as well as on the Ruijsenaars duality of finite many-body integrable models, we review the concept of the integrability and, in particular, of the Lax integrability and we analyze the basic examples of the Yang-Baxter deformations of non-linear sigma-models. The central mathematical structure which we describe in detail is the E-model which is the dynamical system exhibiting all those three phenomena simultaneously. The last part of the paper contains original results, in particular a formulation of sufficient conditions for strong integrability of non-degenerate E-models.

hep-th↗
arXiv2020

T-duality and T-folds for point particles

We argue that the T-duality phenomenon is not exclusively a stringy effect but it is relevant also in the context of the standard point particle dynamics. To illustrate the point, we construct a four-parametric family of four-dimensional electro-gravitational backgrounds such that the dynamics of a charged point particle in those backgrounds is insensitive to a particular permutation of the parameters although this very permutation does alter the background geometry. In particular, we find that a direct product of the Euclidean plane with the two-dimensional Euclidean black hole admits a point-particle T-dual with asymptotically negative curvature. For neutral particles, this point-particle T-duality picture gets slightly modified because the T-duality map is no longer defined everywhere but only on a dense open domain of the space of states. We suggest a possible interpretation of this phenomenon in terms of a point particle T-fold.

hep-th↗
arXiv2019

Dressing cosets and multi-parametric integrable deformations

We provide a new construction of the dressing cosets sigma-models which is based on an isotropic gauging of the E-models. As an application of this new approach, we show that the recently constructed multi-parametric integrable deformations of the principal chiral model are the dressing cosets, they are therefore automatically renormalizable and their dynamics can be completely characterized in terms of current algebras.

hep-th↗
arXiv2017

Yang-Baxter $σ$-model with WZNW term as ${ \mathcal E}$-model

It turns out that many integrable $σ$-models on group manifolds belong to the class of the so-called ${ \mathcal E}$-models which are relevant in the context of the Poisson-Lie T-duality. We show that this is the case also for the Yang-Baxter $σ$-model with WZNW term introduced by Delduc, Magro and Vicedo in \cite{DMV15}.

hep-th↗
arXiv2017

Hidden isometry of "T-duality without isometry"

We study the T-dualisability criteria of Chatzistavrakidis, Deser and Jonke [3] who recently used Lie algebroid gauge theories to obtain sigma models exhibiting a "T-duality without isometry". We point out that those T-dualisability criteria are not written invariantly in [3] and depend on the choice of the algebroid framing. We then show that there always exists an isometric framing for which the Lie algebroid gauging boils down to standard Yang-Mills gauging. The "T-duality without isometry" of Chatzistavrakidis, Deser and Jonke is therefore nothing but traditional isometric non-Abelian T-duality in disguise.

hep-th↗
arXiv2015

$η$ and $λ$ deformations as ${\cal E}$-models

We show that the so called $λ$ deformed $σ$-model as well as the $η$ deformed one belong to a class of the ${\cal E}$-models introduced in the context of the Poisson-Lie-T-duality. The $λ$ and $η$ theories differ solely by the choice of the Drinfeld double; for the $λ$ model the double is the direct product $G\times G$ while for the $η$ model it is the complexified group $G^{\mathbb{C}}$. As a consequence of this picture, we prove for any $G$ that the target space geometries of the $λ$-model and of the Poisson-Lie T-dual of the $η$-model are related by a simple analytic continuation.

hep-th↗
arXiv2013

Quasi-Hamiltonian bookkeeping of WZNW defects

We interpret the chiral WZNW model with general monodromy as an infinite dimensional quasi-Hamiltonian dynamical system. This interpretation permits to explain the totality of complicated cross-terms in the symplectic structures of various WZNW defects solely in terms of the single concept of the quasi-Hamiltonian fusion. Translated from the WZNW language into that of the moduli space of flat connections on Riemann surfaces, our result gives a compact and transparent characterisation of the symplectic structure of the moduli space of flat connections on a surface with k handles, n boundaries and m Wilson lines.

math-ph↗
arXiv2012

On Poisson geometry and supersymmetric sigma models

By using the Poisson geometry, we develop a manifestly invariant and calculation-friendly formalism for handling $UOSp(2|1)$-supersymmetric field theories. In particular, the super-Langrangians are written solely in terms of superfields, Poisson brackets and the moment map generating the $UOSp(2|1)$ action. As an application of this formalism, we construct the Kalb-Ramond term for supersymmetric sigma models on the supersphere.

hep-th↗
arXiv2008

Affine Poisson Groups and WZW Model

We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the $q\to\infty$ limit of the q-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations.

math-ph↗
arXiv2007

$q\to \infty$ limit of the quasitriangular WZW model

We study the $q\to\infty$ limit of the $q$-deformation of the WZW model on a compact simple and simply connected target Lie group. We show that the commutation relations of the $q\to\infty$ current algebra are underlied by certain affine Poisson structure on the group of holomorphic maps from the disc into the complexification of the target group. The Lie algebroid corresponding to this affine Poisson structure can be integrated to a global symplectic groupoid which turns out to be nothing but the phase space of the $q\to\infty$ limit of the $q$-WZW model. We also show that this symplectic grupoid admits a chiral decomposition compatible with its (anomalous) Poisson-Lie symmetries. Finally, we dualize the chiral theory in a remarkable way and we evaluate the exchange relations for the $q\to\infty$ chiral WZW fields in both the original and the dual pictures.

math-ph↗
arXiv2006

u-Deformed WZW Model and Its Gauging

We review the description of a particular deformation of the WZW model. The resulting theory exhibits a Poisson-Lie symmetry with a non-Abelian cosymmetry group and can be vectorially gauged.

math-ph↗