Topological gravity from a transgression gauge field theory

It is shown that a topological action for gravity in even dimensions can be obtained from a gravity theory whose Lagrangian is given by a transgression form invariant under the Poincaré group.     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

Gravity localization in sine-Gordon braneworlds

In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a localized state to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.     

Anomalies, gauge field topology, and the lattice

Motivated by the connection between gauge field topology and the axial anomaly in fermion currents, I suggest that the fourth power of the naive Dirac operator can provide a natural method to define a local lattice measure of topological charge. For smooth gauge fields this reduces to the usual topological density. For typical gauge field configurations in a numerical simulation, however, quantum fluctuations dominate, and the sum of this density over the system does not generally give an integer winding. On cooling with respect to the Wilson gauge action, instanton like structures do emerge. As cooling proceeds, these objects tend shrink and finally “fall through the lattice.” Modifying the action can block the shrinking at the expense of a loss of reflection positivity. The cooling procedure is highly sensitive to the details of the initial steps, suggesting that quantum fluctuations induce a small but fundamental ambiguity in the definition of topological susceptibility.     

Quark masses,the Dashen phase,and gauge field topology

The CP violating Dashen phase in QCD is predicted by chiral perturbation theory to occur when the up–down quark mass difference becomes sufficiently large at fixed down-quark mass. Before reaching this phase, all physical hadronic masses and scattering amplitudes are expected to behave smoothly with the up-quark mass, even as this mass passes through zero. In Euclidean space, the topological susceptibility of the gauge fields is positive at positive quark masses but diverges to negative infinity as the Dashen phase is approached. A zero in this susceptibility provides a tentative signal for the point where the mass of the up quark vanishes. I discuss potential ambiguities with this determination.     

Dynamics of the infinitely-thin kink

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes - implicit collective coordinates - is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.     

Generally covariant vs. gauge structure for conformal field theories

We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group.     

The influence of wire width on the charge distribution of transverse domain walls and their stray field interactions

We present here a numerical study of the magnetostatic charge distribution of transverse Néel type domain wall in permalloy nanowires. The calculations indicate that not only is the distribution highly non-uniform within a given transverse wall but it also varies dramatically with respect to the wire width. The implications of this for magnetostatic domain wall pinning are analyzed by considering the stray field interaction between a wall and another extended magnetic body for a particular domain wall chirality, where two distinct depinning mechanisms are observed depending on the wire width.     

Temperature dependence of switching field distribution in a NiFe wire with a pad

The distribution of switching fields (H_sw) in a NiFe wire was investigated as a function of temperature between 5 and 300 K. The sample structure under investigation is Ta/NiFe/Cu/NiFe wire (150 nm width) connecting to a square pad (large area) at an end. Magnetization reversal phenomena are very sensitively detected using the giant magnetoresistance effect. With repeating magnetoresistance measurements, we obtained a histogram of H_sw with three narrow peaks at each temperature. The origin of three peaks can be attributed to the existence of three different kinds of magnetic domain structures at the pad area, which was confirmed by magnetic force microscopy observation.     

Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F⁺ (H_graviton) where the one-particle Hilbert space H_graviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space H_graviton generated by the gravitational field h and some ghosts fields u, (which are vector Fermi fields) and v (which is a vector Bose field).Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.     

Five Dimensional Domain Walls in a Scalar-Tensor Theory of Gravitation

Five dimensional Kaluza-Klein space-time is considered in the presence of thick domain walls in the framework of scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, [1986]). Exact cosmological model, which represents a stiff domain wall, is presented. Some physical and kinematical properties of the model are also discussed.     

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization.     

The orbit space of the action of gauge transformation group on connections

The behaviour of orbits of the action of the group of smooth gauge transformations on connections for a principal bundle P(M, G) is discussed with and without compactness assumption on M and G. In the case of compact M and with suitable conditions on G a stratification structure for the space of orbits is established. A natural tame weak Riemannian metric is given on each stratum.     

Confinement of the field electron emission to atomic sites on ultra sharp tips

The spatially controlled field assisted etching method for sharpening metallic tips, in a field ion microscope (FIM), is used to study the evolution of the field emission when the tip apex radius is decreased below 1 nm. Unlike the conventional image formation in a field emission microscope (FEM), we demonstrate that at this scale the field emission is rather confined to atomic sites. A single atom apex fabricated at the end of such tips exhibits an outstanding brightness compared to other atomic tips. The measurements have been repeated for two double atom tips, with different atom-atom separations, and images of atomic field emission localization have also been obtained. We have found that the field emission intensity alternates between adjacent atoms when the applied voltage is gradually increased beyond a threshold value.     

Cosmic Strings and Domain Walls in a Scale-Covariant Theory of Gravitation

Axially symmetric space-time is considered in the presence of cosmic string source and thick domain walls in the frame work of a scale-covariant theory of gravitation. A relation between metric potential is assumed to get a determinate solution of the field equations of this theory. In this particular case, it is observed that the geometric (Nambu) string p-string (Takabayasi string) and Reddy string do not survive. It is also seen that the stiff (self-gravitating) domain walls do not exist in this theory.     

Theory of a gravitational gauge field with localization of the de Sitter group

A de Sitter-invariant gauge theory is formulated for the case where a 40-component de Sitter A-field is present. It is shown that the theory coincides with the Poincare-invariant gauge theory in a space with torsion with a cosmological term. Two other versions of a de Sitter-invariant theory are also discussed: the first is a metric theory of gravitation in a Riemann space; the second is a de Sitter-invariant generalization of the tetrad theory of gravitation in a space of absolute parallelism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 50–53, November, 1986.     

Domain wall propagation in Permalloy nanowires with a thickness gradient

The magnetization reversal behavior of Permalloy nanowires has been investigated using a magneto-optic Kerr effect setup. Nanowires with various widths, w=250$w=250$ nm to 3 μm and a thickness of t=10$t=10$ nm were fabricated by electron-beam lithography and subsequent lift-off. Furthermore, similar nanowires but with a thickness gradient along the nanowire axis have been prepared to investigate the influence of the gradient on the magnetic domain wall propagation. Magnetization hysteresis loops recorded on individual nanowires without a gradient are compared to corresponding wires with a thickness gradient. The dependence of the coercive field, _Hc$H_c$ vs. t/w$t/w$ shows a linear behavior for wires without a gradient. However, wires with a gradient display a more complex crossover behavior. We find a plateau in the _Hc$H_c$ vs. t/w$t/w$ curve at values of w$w$, where a transformation from transverse to vortex domain wall type is expected.     

Height gauge based on dual polarization competition laser

Based on dual polarization competition laser, we develop a new height gauge. By inserting a quartz crystal plate into the laser cavity, one laser beam splits into two orthogonally linear polarized laser beams, which appear one after another with the change in cavity length. After detecting their intensities, we obtain two power-turning curves. The longitudinal mode spacing is divided into 4 equal zones and each one has different intensity phenomena, which provides a new method of height measurement. According to experiments, the direct measuring range of this new method is 12 mm with resolution of 79.1 nm, and the indirect measuring range can be increased using first grade gauge blocks and a liftable platform. Compared to other height gauges such as vernier gauge, inductance sensor and gauge block interferometer, this new instrument has the advantage of self-calibration and simple structure without frequency stabilization system.