We show that a suitable background field can bring a non-BPS topological soliton into its BPS, self-dual, counterpart. As an example we consider Skyrmions in the minimal Skyrme model. We prove the triviality of the corresponding moduli space. This means that the resulting self-dual Skyrmion does statically interact with the background field. We also show that the originally self-dual Skyrmions (e.g. solutions of the BPS Skyrme model) can preserve the self-duality after a coupling with a background field. In this case, BPS Skyrmions can be effortless moved with respect to the background.
The BPS baby Skyrme models are submodels of baby Skyrme models, where the nonlinear sigma model term is suppressed. They have skyrmion solutions saturating a BPS bound, and the corresponding static energy functional is invariant under area-preserving diffeomorphisms (APDs). Here we show that the solitons in the BPS baby Skyrme model, which carry a nontrivial topological charge $Q_{b} \in π_2(S^2)$ (a winding number), are dual to vortices in a BPS vortex model with a topological charge $Q_{v}\in π_1(S^1)$ (a vortex number), in the sense that there is a map between the BPS solutions of the two m…
We construct self-dual sectors for scalar field theories on a $(2N+2)$-dimensional Minkowski space-time with target space being the $2N+1$-dimensional sphere $S^{2N+1}$. The construction of such self-dual sectors is made possible by the introduction of an extra functional on the action that renders the static energy and the self-duality equations conformally invariant on the $(2N+1)$-dimensional spatial submanifold. The conformal and target space symmetries are used to build an ansatz that leads to an infinite number of exact self-dual solutions with arbitrary values of the topological charge.…
We introduce a Skyrme type model with the target space being the 3-sphere S^3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space-time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound …
We construct brane solutions in six dimensional Einstein-Skyrme systems. A class of baby skyrmion solutions realize warped compactification of the extra dimensions and gravity localization on the brane for negative bulk cosmological constant. Coupling of the fermions with the brane skyrmions successfully lead to the brane localized fermions. The standard representation of the gamma matrices is used to obtain massive localized modes as well as the massless one. Nonlinear nature of the skyrmions brings richer information for the fermions level structure. In terms of the level crossing picture, e…
In this work we consider the higher dimensional Skyrme model, with spatial dimension $d > 3$, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, \(B\geq 1\), a modified generalized hedgehog ansatz is used where we assign an integer \(n_i\) for each rotational plane, resulting in a topological degree that proportional to product of these integers. It is found via BPS Lagrangian method that there are only two possible BPS submodels for this spherically symmetric ansatz which shall be called as BPS Skyrme model and scale-inva…
We introduce a system composed of two (2+1)-dimensional baby-skyrmion models (BSMs) set on parallel planes and linearly coupled by tunneling of fields. This system can be realized in a dual-layer ferromagnetic medium. Unlike dual-core models previously studied\ in nonlinear optics and BEC, here the symmetry-breaking bifurcation (SBB) in solitons (baby skyrmions) occurs with the increase of the inter-core coupling ($κ$), rather than with its decrease, due to the fact that even in the uncoupled system neither core may be empty. Prior to the onset of the symmetry breaking between the two componen…
We investigate the existence of the skyrmion field in the background of an asymptotically flat stationary reflecting star. For this purpose, we consider the Einstein Skyrme system for which there is a skyrmion hair in the black hole case. We discuss spherically symmetric skyrmions and employ the hedgehog ansatz for the skyrmion field. We show that, in contrast to the black hole there is no skyrmion hair for a reflecting star.
We construct the first analytic examples of topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time-crystals (smooth solutions of the $U(1)$ gauged Skyrme model whose periodic time-dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and …
We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations -- hereafter dubbed Skerrmions -- can be in equilibrium with a Kerr black hole (BH) by virtue of a synchronisation condition. We consider two sectors for Skerrmions. In the sector with non-zero baryon charge, Skerrmions are akin to the known Skyrme solutions on the Schwarzschild background. These `topological' configurations reduce to flat spacetime Skyrmions in a vanishing BH mass limit; moreoever, they never become "small" perturbations on the Kerr background…
A continuous field theory which describes the process of doping in high-T$_c$ superconductors of the YBCO-type is presented. It is shown that the introduction of dopants produces the creation of skyrmion topological excitations on the antiferromagnetic background. The energy of these excitations is evaluated. Destruction of the Néel ground state occurs for a critical value $δ_C$ of the doping parameter for which the skyrmion energy vanishes. We evaluate this at zero temperature, obtaining $δ_C = 0.39 \pm 0.03$ which agrees with the experimental value $δ_C^{exp} = 0.41 \pm 0.02$.
We analyze the high energy scattering of hadrons in QCD in an effective theory model inspired from a gravity dual description. The nucleons are skyrmion-like solutions of a DBI action, and boosted nucleons give pions field shockwaves necessary for the saturation of the Froissart bound. Nuclei are analogs of BIon crystals, with the DBI skyrmions forming a fluid with a fixed inter-nucleon distance. In shockwave collisions one creates scalar (pion field) ``fireballs'' with horizons of nonzero temperature, whose scaling with mass we calculated. They are analogous to the hydrodynamic ``dumb holes,'…
We study radial vibrations of spherically symmetric skyrmions in the BPS Skyrme model. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the BPS Skyrme model already gives a reasonable approximate des…
We investigate properties of self-gravitating isorotating Skyrmions in the generalized Einstein-Skyrme model with higher-derivative terms in the matter field sector. These stationary solutions are axially symmetric, regular and asymptotically flat. We provide a detailed account of the branch structure of the spinning solutions in the topological sector of degree one. We show that additional branches of solutions appear, as the angular frequency increases above some critical value, these "cloudy" configurations can be considered as a bound system of the spinning Skyrmions and "pion" excitations…
This paper investigates a background charge one Skyrme field chirally coupled to light fermions on the 3-sphere. The Dirac equation for the system commutes with a generalised angular momentum or grand spin. It can be solved explicitly for a Skyrme configuration given by the hedgehog form. The energy spectrum and degeneracies are derived for all values of the grand spin. Solutions for non-zero grand spin are each characterised by a set of four polynomials. The paper also discusses the energy of the Dirac sea using zeta function regularization.
We propose a modification of the Skyrme model that supports a self-dual sector possessing exact non-trivial finite energy solutions. The action of such a theory possesses the usual quadratic and quartic terms in field derivatives, but the couplings of the components of the Maurer-Cartan form of the Skyrme model is made by a non-constant symmetric matrix, instead of the usual Killing form of the SU(2) Lie algebra. The introduction of such a matrix make the self-duality equations conformally invariant in three space dimensions, even though it may break the global internal symmetries of the origi…
Diagrammatic rules are developed for simplifying two-loop QED diagrams with propagators in a constant self-dual background field. This diagrammatic analysis, using dimensional regularization, is used to explain how the fully renormalized two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop diagrams. The connection between the two-loop and one-loop vacuum diagrams in a background field parallels a corresponding connection for free vacuum diagrams, without a background field, which can be derived by simple algebraic ma…
We study baryonic matter in holographic QCD with D4/D8/\bar{D8} multi-D brane system in type IIA superstring theory. The baryon is described as the "brane-induced Skyrmion", which is a topologically non-trivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the "truncated-resonance model" approach for the baryon analysis, including pion and ρmeson fields below the ultraviolet cutoff scale M_KK \sim 1GeV, to keep the holographic duality with QCD. We describe the baryonic matter in large N_c as single brane-induced Skyrmion on the three-dimens…
We give the classification of T-duals of the flat background in four dimensions with respect to one-, two-, and three-dimensional subgroups of the Poincaré group using non-Abelian T-duality with spectators. As duals we find backgrounds for sigma models in the form of plane-parallel waves or diagonalizable curved metrics often with torsion. Among others, we find exactly solvable time-dependent isotropic pp-wave, singular pp-waves, or generalized plane wave (K-model).
An exact one monopole solution in a uniform self-dual background field is obtained in the BPS limit of the SU(2) Yang-Mills-Higgs theory by using the inverse scattering method.
We consider the action of a non-abelian T-duality on backgrounds with an AdS${}_5$ factor in type IIA supergravity, finding a new type IIB background, as well as the non-abelian T-dual of a domain wall solution which has as limits the non-abelian T-dual of $AdS_5\times T^{1,1}$ and the non-abelian T-dual of $AdS_3\times \mathbb{R}^2\times S^2\times S^3$. We explore some consequences of non-abelian T-duality for the dual conformal field theories.
We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in 5+1 dimensions. Using the generalized Abelian Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.
We study oscillating string solutions in the Klebanov-Witten and its non-Abelian T-dual background dualised along an SU(2) isometry. We find the string energy as the function of oscillation number and angular momentum. We show that for a particular set of T-dual co-ordinates both the background have equal string states. We also study the string states where the strings are expanding and contracting in the T-dual co-ordinate direction. We expect the presence of the superconformal field theory dual operators whose anomalous dimensions depend on T-dual co-ordinate.
In this paper we consider both Abelian as well as non-Abelian T-duals of the Klebanov-Witten background and inspect their various Penrose limits. We show that these backgrounds admit pp-wave solutions in the neighbourhood of appropriate null geodesics. We study the quantization of closed string propagating on some of the resulting pp-wave backgrounds and comment on the probable field theory duals.
The partition functions of refined topological strings(A-models) are computed, which give rise to the circle-compactified five-dimensional supersymmetric linear quiver gauge theories in generic (not necessarily self-dual) Omega backgrounds. Based on the slicing independence conjecture of refined topological string partition functions, it is demonstrated explicitly that the duality exists between $SU(N)^{M-1}$ and $SU(M)^{N-1}$ supersymmetric linear quiver gauge theories, even in generic Omega backgrounds. It is found that the relations between string moduli and gauge moduli are deformed from t…
In this work we study mesonic excitations in a Quantum Field Theory dual to the non Abelian T-dual of $AdS_5\times S^5$, using a D6 brane probe on the Sfetsos-Thompson background. Before and after the duality, we observe interesting differences between the spectra and interpret them. The spectrum of masses and the interactions among mesonic excitations teach valuable lessons about the character of non-Abelian T-duality and its implications for Holography. The case of Abelian T-duality is also studied.
We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma-models on AdS backgrounds with Ramond-Ramond fluxes in various dimensions. We show that sigma-models based on supercosets of PSU supergroups, such as AdS_2 \times S^2 and AdS_3 \times S^3 are self-dual under fermionic T-duality, while supercosets of OSp supergroups such as non-critical AdS_2 and AdS_4 models, and the critical AdS_4 \times CP^3 background are not. We present a general algebraic argument to when a supercoset is expected to have a fermionic T-duality symmetry, and when it will fail to have one.
We find new type II backgrounds with non-relativistic symmetries via non-Abelian T-duality. First we consider geometries with Galilean symmetries in type IIA, which have been identified as non-relativistic generalizations of the ABJM background and massive IIA supergravities. We then consider the non-Abelian T-duality transformation on the backgrounds with Lifshitz symmetry constructed by Donos and Gauntlett. Using gauge/gravity duality we study aspects of the field theory dual to these backgrounds.
In the paper [1] we showed that in double space, where all initial coordinates $x^μ$ are doubled $x^μ\to y_μ$, the T-duality transformations can be performed by exchanging places of some coordinates $x^a$ and corresponding dual coordinates $y_a$. Here we generalize this result to the case of weakly curved background where in addition to the extended coordinate we will also transform extended argument of background fields with the same operator $\hat {\cal T}^a$. So, in the weakly curved background T-duality leads to the physically equivalent theory and complete set of T-duality transformations…
In this paper we consider the Klebanov-Tseytlin background and its non-Abelian T-dual geometry along a suitably chosen $SU(2)$ subgroup of isometries. We analyse the Penrose limits along various null geodesics of both the geometries. We observe that, the Klebanov-Tseytlin geometry does not admit any pp-wave solutions. However, the T-dual background gives rise to pp-wave solution upon taking the Penrose limit along some appropriate null geodesic. We comment on the possible gauge theory dual for our pp-wave background.
We construct the low-energy effective field theory for a D3-brane in constant R-R 2-form potential background as the S-dual theory of a D3-brane in NS-NS B-field background. Despite the non-Abelian algebra of the noncommutative U(1) gauge symmetry, the electromagnetic duality transformation can be carried out to all orders, and the dual Lagrangian is given in a compact form. The gauge algebra is found to be a mixture of a deformed area-preserving diffeomorphism and the usual U(1) gauge symmetry.
We give exact solutions for a recently developed ~$N=1$~ locally supersymmetric self-dual gauge theories in $~(2+2)\-$dimensions. We give the exact solutions for an $~SL(2)$~ self-dual Yang-Mills multiplet and what we call ``self-dual tensor multiplet'' on the gravitational instanton background by Eguchi-Hanson. We use a general method to get an $~SL(2)$~ self-dual Yang-Mills solution from any known self-dual gravity solution. Our result is the first example of exact solutions for the coupled system of these $~N=1$~ locally supersymmetric self-dual multiplets in ~$(2+2)\-$dimensions, which is …
By addition of non-zero, but torsionless $B$-field, we expand the classification of (non-)Abelian T-duals of the flat background in four dimensions with respect to one-, two-, three-, and four-dimensional subgroups of Poincaré group. We discuss the influence of the additional $B$-field on the process of dualization and identify essential parts of the torsionless $B$-field that cannot be eliminated in general by coordinate or gauge transformation of the dual background. These effects are demonstrated using particular examples. Due to their physical importance, we focus on duals whose metrics re…
We consider a theory of an open string moving in a weakly curved background, composed of a constant metric and a linearly coordinate dependent Kalb-Ramond field with an infinitesimal field strength. We find its T-dual using the generalized Buscher procedure developed for the closed string moving in a weakly curved background, and the fact that solving the boundary conditions, the open string theory transforms to the effective closed string theory. So, T-dualizing the effective theory along all effective directions we obtain its T-dual theory and resume the open sting theory which has such an e…
We find an explicit supergravity background dual to the $Ω$-deformation of a four-dimensional $\mathcal{N}=2$ SCFT on $\mathbb{R}^4$. The solution can be constructed in the five-dimensional ${\cal N}=4^+$ gauged supergravity and has a nontrivial self-dual 2-form. When uplifted to type IIB supergravity the background is a deformation of AdS$_5\times S^5$ which preserves 16 supercharges. We also discuss generalizations of this solution corresponding to turning on a vacuum expectation value for a scalar operator in the dual SCFT.
We discuss T-duality for open strings in general background fields both in the functional integral formulation as well as in the language of canonical transformations. The Dirichlet boundary condition in the dual theory has to be treated as a constraint on the functional integration. Furthermore, we give meaning to the notion of matrix valued string end point position in the presence of nonabelian gauge field background.
We give a classification of non-Abelian T-duals of the flat metric in D=4 dimensions with respect to the four-dimensional continuous subgroups of the Poincare group. After dualizing the flat background, we identify majority of dual models as conformal sigma models in plane-parallel wave backgrounds, most of them having torsion. We give their form in Brinkmann coordinates. We find, besides the plane-parallel waves, several diagonalizable curved metrics with nontrivial scalar curvature and torsion. Using the non-Abelian T-duality, we find general solution of the classical field equations for all…
Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3 dimensional self-dual space-like warped $AdS_3$ black hole background. We argue that in this background, symmetric conditions and gauge constraint can not be satisfied simultaneously. Using new suitable constraint, we find the exact solutions of equation of motion. Then, we obtain the quasi-normal modes by imposing appropriate boundary condition at horizon and infinity.
A new solution in the string background dual to N=1 SQCD-like theories is presented. The gauge coupling in this solution has walking property. The Wilson loop calculations show that quark anti-quark potential makes phase transitions. Additionally the effect of flavours on other solutions in this background is investigated by considering some unflavoured solutions and perturbing them with small parameter $x=\frac{N_{f}}{N_{c}}$.
We consider non-Abelian T-duality on N=1 supergravity backgrounds possessing well understood field theory duals. For the case of D3-branes at the tip of the conifold, we dualise along an SU(2) isometry. The result is a type-IIA geometry whose lift to M-theory is of the type recently proposed by Bah et. al. as the dual to certain N=1 SCFT quivers produced by M5-branes wrapping a Riemann surface. In the non-conformal cases we find smooth duals in massive IIA supergravity with a Romans mass naturally quantised. We initiate the interpretation of these geometries in the context of the AdS/CFT corre…
In this paper we study aspects of geometries in Type IIA and Type IIB String theory and elaborate on their field theory dual pairs. The backgrounds are associated with reductions to Type IIA of solutions with $G_2$ holonomy in eleven dimensions. We classify these backgrounds according to their G-structure, perform a non-Abelian T-duality on them and find new Type IIB configurations presenting {\it dynamical} $SU(2)$-structure. We study some aspects of the associated field theories defined by these new backgrounds. Various technical details are clearly spelled out.
This paper describes the background field equations for strings in T-duality symmetric formalisms in which the dimension of target space is doubled and the sigma model supplemented with constraints. These are calculated by demanding the vanishing of the beta-functional of the sigma model couplings in the doubled target space. We demonstrate the equivalence with the background field equations of the standard string sigma model.
A geometrical approach in the non-symmetric connection framework is employed to examine the issue of higher order $α'$ corrections to D=10 type IIB superstring backgrounds with a covariantly constant null Killing isometry and non-zero Ramond-Ramond field content. These describe generalized supersymmetric string waves and were obtained recently by us through the S-duality transformation of purely NS-NS plane wave backgrounds. We find that the backgrounds are exact subject to the existence of certain field redefinitions and provided certain restrictive conditions are satisfied.
We show that the super D3-brane action on $AdS_5 \times S^5$ background recently constructed by Metsaev and Tseytlin is exactly invariant under the combination of the electric-magnetic duality transformation of the worldvolume gauge field and the SO(2) rotaion of N=2 spinor coordinates. The action is shown to satisfy the Gaillard-Zumino duality condition, which is a necessary and sufficient condition for a action to be self-dual. Our proof needs no gauge fixing for the $κ$-symmetry.
We investigate plane-parallel wave metrics from the point of view of their (Poisson-Lie) T-dualizability. For that purpose we reconstruct the metrics as backgrounds of nonlinear sigma models on Lie groups. For construction of dual backgrounds we use Drinfel'd doubles obtained from the isometry groups of the metrics. We find dilaton fields that enable to satisfy the vanishing beta equations for the duals of the homogenous plane-parallel wave metric. Torsion potentials or B-fields, invariant w.r.t. the isometry group of Lobachevski plane waves are obtained by the Drinfel'd double construction. W…
We establish the consistency of duality transformations for generic systems of $N=2$ vector supermultiplets in the presence of a chiral background field. This is relevant, for instance, when dealing with spurion fields or when considering higher-derivative couplings of vector multiplets to supergravity. We point out that under duality most quantities do not transform as functions. With few exceptions, true functions are nonholomorphic, even though the duality transformations themselves are holomorphic in nature.
We present the action for a self-dual tensor in six dimensions, coupled to a (2,0) conformal supergravity background. This action gives rise to the expected equations of motion. An alternative look upon one of the gauge symmetries clarifies its role in the supersymmetry transformation rules and the realisation of the algebra.
In one of our previous papers we generalized the Buscher T-dualization procedure. Here we will investigate the application of this procedure to the theory of a bosonic string moving in the weakly curved background. We obtain the complete T-dualization diagram, connecting the theories which are the result of the T-dualizations over all possible choices of the coordinates. We distinguish three forms of the T-dual theories: the initial theory, the theory obtained T-dualizing some of the coordinates of the initial theory and the theory obtained T-dualizing all of the initial coordinates. While the…
We consider the closed string propagating in the weakly curved background which consists of constant metric and Kalb-Ramond field with infinitesimally small coordinate dependent part. We propose the procedure for constructing the T-dual theory, performing T-duality transformations along coordinates on which the Kalb-Ramond field depends. The obtained theory is defined in the non-geometric double space, described by the Lagrange multiplier $y_μ$ and its $T$-dual $\tilde{y}_μ$. We apply the proposed T-duality procedure to the T-dual theory and obtain the initial one. We discuss the standard rela…
We study fermionic zero modes in the background of self-dual vortex on a two-dimensional non-compact extra space in 5+1 dimensions. In the Abelian Higgs model, we present an unified description of the topological and non-topological self-dual vortex on the extra two dimensions. Based on it, we study localization of bulk fermions on a brane with inclusion of Yang-Mills and gravity backgrounds in six dimensions. Through two simple cases, it is shown that the vortex background contributes a phase shift to the fermionic zero mode, this phase is actually origin from the Aharonov-Bohm effect.
By using the self-dual vortex background on extra two-dimensional Riemann surfaces in 5+1 dimensions, the localization mechanism of bulk fermions on a string-like defect with the exponentially decreasing warp-factor is obtained. We give the conditions under which localized spin 1/2 and 3/2 fermions can be obtained.
