The principal sigma model and Abelian gauge fields coupling is studied. By expressing the first-order formulation of the gauge field equations an implicit on-shell scalar-gauge field decoupling structure is revealed. It is also shown that due to this decoupling structure the scalars of the theory belong to the pure sigma model and the gauge fields sector consists of a number of coupled Maxwell theories with currents partially induced by the scalars.
In this work we study a nonlinear gauged O(3)-sigma model with both minimal and nonminimal coupling in the covariant derivative. Using an asymmetric scalar potential, the model is found to exhibit both topological and non-topological soliton solutions in the Bogomol'nyi limit.
In this work we consider an Abelian O(3) sigma model coupled nonminimally with a gauge field governed by a Maxwell and Chern-Simons terms. Bogomol'nyi equations are constructed for a specific form of the potential and generic nonminimal coupling constant. Furthermore, topological and nontopological self-dual soliton solutions are obtained for a critical value of the nonminimal coupling constant. Some particular static vortex solutions (topological and nontopological) satisfying the Bogomol'nyi bound are numerically solved and presented.
We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell's term and subject to a so-called Gausson's self-dual potential. To carry out this study, it is numerically shown that this model supports topological solutions in 3-dimensional spacetime. In fact, to obtain the topological solutions, we assume a spherically symmetrical ansatz to find the solutions, as well as some physical behaviors of the vortex, as energy and magnetic field. It is presented a planar view of the magnetic field as an interesting…
We study the supersymmetric extension of the gauged $ O(3) $ sigma model in $ 2+1 $ dimensions and find the supersymmetry algebra. We also discuss soliton solutions in case the Maxwell term is replaced by the Born-Infeld term. We show that by appropriate choice of the potential, the self-dual equations in the Born-Infeld case coincide with those of the Maxwell's case.
We construct static multicenter solutions of phantom Einstein-Maxwell-dilaton theory from null geodesics of the target space, leading to regular black holes without spatial symmetry for certain discrete values of the dilaton coupling constant. We also discuss the three-dimensional gravitating sigma models obtained by reduction of phantom Einstein-Maxwell, phantom Kaluza-Klein and phantom Einstein-Maxwell-dilaton-axion theories. In each case, we generate by group transformations phantom charged black hole solutions from a neutral seed.
We consider a (2+1) dimensional nonlinear O(3) sigma model with its U(1) subgroup gauged along with the inclusion of a self-interaction having symmetry breaking minima.The gauge field dynamics is governed by the Maxwell term.The model is shown to support topologically stable purely magnetic self-dual vortices.
We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that a…
We introduce the self-dual abelian gauged $O(3)$ sigma models where the Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge field. These models have quite rich structures and various limits. Our models are found to exhibit both symmetric and broken phases of the gauge group. We discuss the pure Chern-Simons limit in some detail and study rotationally symmetric solitons.
Gauged linear sigma models with C^m-valued scalar fields and gauge group U(1)^d, d \leq m, have soliton solutions of Bogomol'nyi type if a suitably chosen potential for the scalar fields is also included in the Lagrangian. Here such models are studied on (2+1)-dimensional Minkowski space. If the dynamics of the gauge fields is governed by a Maxwell term the appropriate potential is a sum of generalised Higgs potentials known as Fayet-Iliopoulos D-terms. Many interesting topological solitons of Bogomol'nyi type arise in models of this kind, including various types of vortices (e.g. Nielsen-Oles…
We describe a method to remove non-decoupling heavy fields from a quantized field theory and to construct a low-energy one-loop effective Lagrangian by integrating out the heavy degrees of freedom in the path integral. We apply this method to the Higgs boson in a spontaneously broken SU(2) gauge theory (gauged linear sigma-model). In this context, the background-field method is generalized to the non-linear representation of the Higgs sector by applying (a generalization of) the Stueckelberg formalism. The (background) gauge-invariant renormalization is discussed. At one loop the log M_H-terms…
Magnetized Baryonic layer and a novel BPS bound in the gauged-Non-Linear-Sigma-Model-Maxwell theory in (3+1)-dimensions through Hamilton-Jacobi equation
The scale invariance of the $O(3)$ sigma model can be broken by gauging a $U(1)$ subgroup of the $O(3)$ symmetry and including a Maxwell term for the gauge field in the Lagrangian. Adding also a suitable potential one obtains a field theory of Bogomol'nyi type with topological solitons. These solitons are stable against rescaling and carry magnetic flux which can take arbitrary values in some finite interval. The soliton mass is independent of the flux, but the soliton size depends on it. However, dynamically changing the flux requires infinite energy, so the flux, and hence the soliton size, …
We show that the degenerate positive-norm physical propagating fields of the open bosonic string can be gauged to the higher rank fields at the same mass level. As a result, their scattering amplitudes can be determined from those of the higher spin fields. This phenomenon arises from the existence of two types of zero-norm states with the same Young representations as those of the degenerate positive-norm states in the old covariant first quantized (OCFQ) spectrum. This is demonstrated by using the lowest order gauge transformation of Witten's string field theory (WSFT) up to the fourth massi…
For the study of topological vortices with non-minimal coupling, we built a kind of non-canonical O(3)-sigma model, with a Maxwell term modified by a dielectric function. Through the BPS formalism, an investigation is made on possible configurations of vortices in topological sectors of the sigma model and the real scalar field. For a particular ansatz, the solutions of the topological sector of the real scalar field are described by the known kink solutions. On the other hand, when studying the vortices in the non-minimal sector of the pure O(3)-sigma model, it is detected the emergence of so…
We explain how to obtain new classical integrable field theories by assembling two affine Gaudin models into a single one. We show that the resulting affine Gaudin model depends on a parameter $γ$ in such a way that the limit $γ\to 0$ corresponds to the decoupling limit. Simple conditions ensuring Lorentz invariance are also presented. A first application of this method for $σ$-models leads to the action announced in [Phys. Rev. Lett. 122 (2019) 041601] and which couples an arbitrary number $N$ of principal chiral model fields on the same Lie group, each with a Wess-Zumino term. The affine Gau…
We identify a regime of the AdS/CFT correspondence in which we can quantitatively match N=4 super Yang-Mills (SYM) for small 't Hooft coupling with weakly coupled type IIB string theory on AdS_5 x S^5. We approach this regime by taking the same decoupling limit on both sides of the correspondence. On the gauge theory side only the states in the SU(2) sector survive, and in the planar limit the Hamiltonian is given by the XXX_{1/2} Heisenberg spin chain. On the string theory side we show that the decoupling limit corresponds to a non-relativistic limit. In this limit some of the bosonic modes a…
We investigate the decoupling limit in the DGP model of gravity by studying its nonlinear equations of motion. We show that, unlike 4D massive gravity, the limiting theory does not reduce to a sigma model of a single scalar field: Non-linear mixing terms of the scalar with a tensor also survive. Because of these terms physics of DGP is different from that of the scalar sigma model. We show that the static spherically-symmetric solution of the scalar model found in hep-th/0404159, is not a solution of the full set of nonlinear equations. As a consequence of this, the interesting result on hidde…
Non-linear sigma models with scalar fields taking values on $\mathbb{C}\mathbb{P}^n$ complex manifolds are addressed. In the simplest $n=1$ case, where the target manifold is the $\mathbb{S}^2$ sphere, we describe the scalar fields by means of stereographic maps. In this case when the $\mathbb{U}(1)$ symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnet…
We use the notion of the gauge/string duality and discuss the Liouvillian (non) integrability criteria for string sigma models in the context of recently proposed Arutyunov-Bassi-Lacroix (ABL) model [JHEP \textbf{03} (2021), 062]. Our analysis complements those previous results due to numerical analysis as well as Lax pair formulation. We consider a winding string ansatz for the deformed torus $T^{\qty(λ_{1},λ_{2},λ)}_{k}$ which can be interpreted as a system of coupled pendulums. Our analysis reveals the Liouvillian nonintegrablity of the associated sigma model. We also obtain the \emph{gener…
We complete a metric-free axiomatic framework for electrodynamics by introducing the appropriate energy-momentum current Sigma of the electromagnetic field. We start from the Lorentz force density and motivate the form of Sigma. Then we postulate it (fourth axiom) and discuss its properties. In particular, it is found that Sigma is traceless and invariant under an electric-magnetic reciprocity transformation. By using the Maxwell-Lorentz spacetime relation (fifth axiom), Sigma is also shown to be symmetric, that is, it has 9 independent components
We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-type hyperbolic systems (including the 2D Toda chains), and Euler-Lagrange gauge theories (such as the Yang-Mills theories, gravity, or the Poisson sigma-models). Also, we formulate several open problems.
We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion $π$ over space-time, whose total space carries a Lorentzian metric making the fibers into totally-geodesic connected Riemannian submanifolds. In particular, $π$ is a fiber bundle endowed with a complete Ehresmann connection whose transport acts through isometries between the fibers. In turn, the Abelian gauge fields are "twisted"…
The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are presented. The complete set of seven coupled non-linear field equations of the gauged non-linear sigma model together with the corresponding Maxwell equations are reduced in a self-consistent way to just one linear Schrodinger-like equation in two dimensions. The corresponding two dimensional periodic potential can be computed explicitly in terms of the solitons …
In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the 'heavy' directions on the low energy dynamics arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the full theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the path followed by the fields can still have a profound influen…
We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma models with closed target manifolds supporting a Riemannian metric, dilaton, and 2-form B-field. By generalizing recent mathematical results to incorporate the B-field and by decoupling the dilaton, we are able to describe the 1-loop beta-functions of the metric and B-field as the components of the gradient of a potential functional on the space of coupling constants. We emphasize a special choice of diffeomo…
We study some symmetry and integrability properties of four-dimensional Einstein-Maxwell gravity with nonvanishing cosmological constant in the presence of Killing vectors. First of all, we consider stationary spacetimes, which lead, after a timelike Kaluza-Klein reduction followed by a dualization of the two vector fields, to a three-dimensional nonlinear sigma model coupled to gravity, whose target space is a noncompact version of $\mathbb{C}\text{P}^2$ with SU(2,1) isometry group. It is shown that the potential for the scalars, that arises from the cosmological constant in four dimensions, …
In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by the perturbative approach, we investigate the existence of topological structures in the cuscuton-like model. The structures we study are, first, kink-like configurations in two dimensional spacetime, second, vortex solutions in three dimensional one with gauge field ruled by the Maxwell term. In fact, to show the existence of kink solutions it is needed to i…
In this paper, we construct the first analytic examples of (3+1)-dimensional self-gravitating regular cosmic tube solutions which are superconducting, free of curvature singularities and with non-trivial topological charge in the Einstein-SU(2) non-linear sigma-model. These gravitating topological solitons at a large distance from the axis look like a (boosted) cosmic string with an angular defect given by the parameters of the theory, and near the axis, the parameters of the solutions can be chosen so that the metric is singularity free and without angular defect. The curvature is concentrate…
We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector bundle $(\mathcal{S},D,ω)$ defined over the scalar manifold $\mathcal{M}$. The construction uses a taming of $(\mathcal{S}, ω)$, which encodes globally the inverse gauge couplings and theta angles of the "twisted" Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give cl…
Chiral--Maxwell Cavity EFT: Reduced Gauge-Mode Condensation and Quantum-Optics Limits
Centro de Estudios Científicos (CECs)（科学研究中心）；Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Instituto de Ciencias Básicas, Facultad de Ingeniería y Ciencias, Universidad Diego Portales（迭戈帕托莱斯大学工程与科学学院基础科学研究所）
We investigate the existence of vortex configurations in two gauged-$CP(2)$ models extended via the inclusion of magnetic impurities. In particular, we consider both the Maxwell-$CP(2)$ and the Chern-Simons-$CP(2)$ enlarged scenarios, separately. We choose a $CP(2)$-field configuration with a null topological charge not only in the simplest (free) case, but also when coupled to an Abelian gauge field. The implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism shows that the effective models for such a configuration possess a self-dual structure which looks like those inherent to …
This study revisits the absorption and scattering process by which a massless scalar field impinges on a charged dilatonic black hole. First, we review the classical analysis to obtain the deflection angle and the differential scattering cross-section. Then, using the partial wave method, we determine the total absorption cross-section numerically in terms of the decoupling parameter called $Mω$, finding that the amplitude of the dilatonic black hole is lower than the Reissner-Nordström one for mild frequencies. In the high-frequency limit, the absorption cross-section exhibits two different c…
We derive the Thermodynamic Bethe Ansatz equations for the relativistic sigma model describing the AdS(4)XCP(3) string II A theory at strong coupling (i.e. in the Alday-Maldacena decoupling limit). The corresponding Y-system involves an infinite number of Y functions and is of a new type, although it shares a peculiar feature with the Y-system for AdS(4)XCP(3). A truncation of the equations at level p and a further generalisation to generic rank N allow us an alternative description of the theory as the N=4, p= \infty representative in an infinite family of models corresponding to the conforma…
We present a method to generate static solutions in the Einstein-Maxwell system with a (phantom) dilaton field in $n(\ge 4)$-dimensions, based upon the symmetry of the target space for the nonlinear sigma model. Unlike the conventional Einstein-Maxwell-dilaton system, there appears a critical value of the coupling constant for a phantom dilaton field. In the noncritical case, the target space is $\mathbb R\times {\rm SL}(2,\mathbb R)/H$ with the maximal subgroup $H=\{{\rm SO}(2), {\rm SO}(1,1)\}$, whereas in the critical case the target space becomes a symmetric pp-wave and the corresponding K…
