First order parent formulation for generic gauge field theories

We show how a generic gauge field theory described by a BRST differential can systematically be reformulated as a first order parent system whose spacetime part is determined by the de Rham differential. In the spirit of Vasiliev's unfolded approach, this is done by extending the original space of fields so as to include their derivatives as new independent fields together with associated form fields. Through the inclusion of the antifield dependent part of the BRST differential, the parent formulation can be used both for on and off-shell formulations. For diffeomorphism invariant models, the parent formulation can be reformulated as an AKSZ-type sigma model. Several examples, such as the relativistic particle, parametrized theories, Yang-Mills theory, general relativity and the two dimensional sigma model are worked out in details.Comment: 36 pages, additional sections and minor correction

Parent formulation at the Lagrangian level

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected, references adde

Magneto-Optical and Multiferroic Properties of Transition-Metal (Fe, Co, or Ni)-Doped ZnO Layers Deposited by ALD

ZnO doped with transition metals (Co, Fe, or Ni) that have non-compensated electron spins attracts particular interest as it can induce various magnetic phenomena and behaviors. The advanced atomic layer deposition (ALD) technique makes it possible to obtain very thin layers of doped ZnO with controllable thicknesses and compositions that are compatible with the main microelectronic technologies, which further boosts the interest. The present study provides an extended analysis of the magneto optical MO Kerr effect and the dielectric properties of (Co, Fe, or Ni)-doped ZnO films prepared by ALD. The structural, magneto optical, and dielectric properties were considered in relation to the technological details of the ALD process and the corresponding dopant effects. All doped samples show a strong MO Kerr behavior with a substantial magnetization response and very high values of the Kerr polarization angle, especially in the case of ZnO/Fe. In addition, the results give evidence that Fe-doped ZnO also demonstrates a ferroelectric behavior. In this context, the observed rich and versatile physical nature and functionality open up new prospects for the application of these nanostructured materials in advanced electronic, spintronic, and optical devices

Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring

We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde

Rigid Supersymmetric Theories in Curved Superspace

We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $\mathcal{M}$, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For $\mathcal{M}=AdS_4$ we reproduce the known results in the literature. A supersymmetric Lagrangian for $\mathcal{M}=\mathbb{S}^4$ exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for $\mathcal{M}=\mathbb{S}^3\times \mathbb{R}$ and note that the time direction $\mathbb{R}$ can be rotated to Euclidean signature and be compactified to $\S^1$ only when the theory has a continuous R-symmetry. The partition function on $\mathcal{M}=\mathbb{S}^3\times \S^1$ is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant $\mathcal{N}=2$ theories on $\mathbb{S}^3$ and clarify a few points about them.Comment: 26 pages, uses harvmac; v2 with added reference

Vortices and chirality of magnetostatic modes in quasi-2D ferrite disk particles

In this paper we show that the vortex states can be created not only in magnetically soft "small" (with the dipolar and exchange energy competition) cylindrical dots, but also in magnetically saturated "big" (when the exchange is neglected) cylindrical dots. A property associated with a vortex structure becomes evident from an analysis of confinement phenomena of magnetic oscillations in a ferrite disk with a dominating role of magnetic-dipolar (non-exchange-interaction) spectra. In this case the scalar (magnetostatic-potential) wave functions may have a phase singularity in a center of a dot. A non-zero azimuth component of the flow velocity demonstrates the vortex structure. The vortices are guaranteed by the chiral edge states of magnetic-dipolar modes in a quasi-2D ferrite disk

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE

From correlation functions to Wilson loops

We start with an n-point correlation function in a conformal gauge theory. We show that a special limit produces a polygonal Wilson loop with $n$ sides. The limit takes the $n$ points towards the vertices of a null polygonal Wilson loop such that successive distances $x^2_{i,i+1} \to 0$. This produces a fast moving particle that generates a "frame" for the Wilson loop. We explain in detail how the limit is approached, including some subtle effects from the propagation of a fast moving particle in the full interacting theory. We perform perturbative checks by doing explicit computations in N=4 super-Yang-Mills.Comment: 37 pages, 10 figures; typos corrected, references adde

(1,0) superconformal models in six dimensions

We construct six-dimensional (1,0) superconformal models with non-abelian gauge couplings for multiple tensor multiplets. A crucial ingredient in the construction is the introduction of three-form gauge potentials which communicate degrees of freedom between the tensor multiplets and the Yang-Mills multiplet, but do not introduce additional degrees of freedom. Generically these models provide only equations of motions. For a subclass also a Lagrangian formulation exists, however it appears to exhibit indefinite metrics in the kinetic sector. We discuss several examples and analyze the excitation spectra in their supersymmetric vacua. In general, the models are perturbatively defined only in the spontaneously broken phase with the vev of the tensor multiplet scalars serving as the inverse coupling constants of the Yang-Mills multiplet. We briefly discuss the inclusion of hypermultiplets which complete the field content to that of superconformal (2,0) theories.Comment: 30 pages, v2: Note, some comments and references adde