Witten's gauge field equations and an infinite-dimensional Grassmann manifold

Witten's gauge fields are interpreted as motions on an infinite-dimensional Grassmann manifold. Unlike the case of self-dual Yang-Mills equations in Takasaki's work, the initial data must satisfy a system of differential equations since Witten's equations comprise a pair of spectral parameters. Solutions corresponding to (anti-) self-dual Yang-Mills fields are characterized in the space of initial data and in application, some Yang-Mills fields which are not self-dual, anti-self-dual nor abelian can be constructed.     

Constant gauge fields and their quantum fluctuations

We analyze the vacuum fluctuations generated by translation-invariant gauge fields and show that these fields are unstable unless they are (anti-)self-dual and abelian. Self-dual constant fields support infinitely many zero modes analogous to instantons. The quantum corrections to the classical action are worked out in the one-loop approximation.     

Wave Function of Non-Vacuum Universe in Ashtekar Theory

In this paper, we studied the wave function of the universe in the (anti-) self-dual representation for the cosmological-model in which the closed Robertson- Walker spacetime is minimally coupled to a massless scalar field and the cosmological constant is equal to zero. We found that some wave functions in the (anti-) self-dual representation cannot be mapped into the σ-representation, or the metric representation, and vice versa.     

Double Self-Dual and Anti-Self-Dual Structure of N=1 Supergravity

Using the Dirac matrices the double self-dual and anti-self-dual structure of N=1 supergravity is discussed. It is shown that the (anti-)self-dual part of the curvature does not consist of the (anti-)self-dual part of the connection alone, and the (anti-)self-dual part of the Lagrangian quadratic in the curvature consists of the (anti-)self-dual part of the curvature alone only when the Lagrangian does not include torsion terms if the torsion of the spacetime does not vanish. Such a new Lagrangian is constructed. It includes no Einstein-Hilbert term but its self-dual part contains an Ashtekar term.     

Analytic loops and gauge fields

In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We show that such representations are closely associated with the (anti-)self-dual Yang–Mills equations in R⁸.     

Parametric (Anti-) Self-Dual Variables and a Related Parametric Yang–Mills–Like Action in Four-Dimensional Gravity

Internal and external parametric dualtransformations as well as (anti-) self-dual variablesin four-dimensional gravity are presented in a unifiedway via a parameter. The double complex (anti-)self-dual variables including the double complex Ashtekarvariables are studied by using the double complexfunction method. Concretely, a parametricYang–Mills-like action is proposed and theanalytic continuation from a double action to the Euclidean action isdiscussed. Some results of previous gravitationaltheories are extended to a parametric form.     

Double Complex (Anti-)self-dual Variables and a Related Double Action in Four-dimensional Gravity

In this paper double dual transformations anddouble complex (anti-)self-dual variables infour-dimensional gravity are given by using the doublecomplex function method. A double action with doublecomplex anti-self-dual variables is proposed, hence thedouble complex (anti-) self-dual gravitational theory isestablish. Finally, the analytic continuation from thedouble action to the Euclidean action is discussed, and some given results are here extended intoa double form.     

Symmetry breaking by instantons in supergravity

The non-zero modes of different spin operators on the background of a self-dual gravitational instanton are all related by global supersymmetry transformations and completely cancel in the one-loop term, which is determined entirely by the zero modes. We derive the number of zero modes of each spin. In an asymptotically locally Euclidean self-dual instanton there are 2τ $\text{spin}\text{-}\text{3}\text{2}$ zero modes and 3τ spin-2 zero modes, where τ is the Hirzebruch signature. Up to 3 of the spin-2 zero modes (depending on boundary conditions) may correspond to global rotations. The $\text{spin}\text{-}\text{3}\text{2}$ zero modes break the U(1) chiral symmetry and give rise to helicity-changing amplitudes. Together with the spin-2 zero modes they determine the trace anomaly or scaling behaviour. We can compare our results with the perturbation theory predictions for the axial vector current and trace anomalies in K3, the unique compact self-dual gravitational instanton, because in this case there are no boundary terms. We obtain agreement.     

Noncommutative AKNS Equation Hierarchy and Its Integrable Couplings with Kronecker Product

We present a noncommutative version of the Ablowitz-Kaup-Newell-Segur （AKNS） equation hierarchy, which possesses the zero curvature representation. Furthermore, we derive the noncommutative AKNS equation from the noncommutative （anti-）self-dual Yang-Mills equation by reduction, which is an evidence for the noncommutative Ward conjecture. Finally, the integrable coupling system of the noncommutative AKNS equation hierarchy is constructed by using the Kronecker product.     

Fermionic Zero Modes in Self-dual Vortex Background on a Torus

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.     

Einstein-Weyl from Kaluza-Klein

We discuss the Kaluza-Klein reduction of spaces with (anti-)self-dual Weyl tensor and point out the emergence of the Einstein-Weyl equations for the reduction from four to three dimensions. As a byproduct we get a simple expression for the gravitational instanton density in terms of the Kaluza-Klein functions.     

Anisotropic electron-phonon interaction in the cuprates

We explore manifestations of electron-phonon coupling on the electron spectral function for two phonon modes in the cuprates exhibiting strong renormalizations with temperature and doping. Applying simple symmetry considerations and kinematic constraints, we find that the out-of-plane, out-of-phase O buckling mode (B(1g)) involves small momentum transfers and couples strongly to electronic states near the antinode while the in-plane Cu-O breathing modes involve large momentum transfers and couples strongly to nodal electronic states. Band renormalization effects are found to be strongest in the superconducting state near the antinode, in full agreement with angle-resolved photoemission spectroscopy data.     

Finite Size Effects in the Free Energy Density for Abelian (Anti-)Self-Dual Gluon Field in SU(3) Gluodynamics

Physics of Particles and Nuclei Letters - Finite-size effects in the free energy density for Abelian (anti-)self-dual gluon field are investigated within $$SU(3)$$ gluodynamics. In particular, the...     

Transition matrices of self-dual solutions to SU(N) gauge theory

We extract self-dual potentials from SU(N) transition matrices of the Atiyah—Ward type. The simplest nontrivial example is studied in detail and we find a topologically nontrivial, regular, self-dual solution. Different gauges can be found for which the corresponding gauge potentials are respectively time-independent or real.     

Almost Everywhere Homogeneous Abelian (Anti)Self-Dual Fields as a Domain Wall Network

Physics of Particles and Nuclei Letters - The properties of a statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual fields represented in the form of a domain wall network...     

Lasing modes in a spiral-shaped dielectric microcavity

The resonance patterns and lasing modes in a spiral-shaped dielectric microcavity are investigated through passive and active medium calculations. We find that the high-Q resonance modes are whispering-gallery-like modes, and these resonance modes can be easily excited as lasing modes. We also find that the quasi-scarred resonance mode, which shows strong directional emission beams from the cavity boundary, can be excited with selectively applied external pumping. Through a spectral analysis of the time evolution of the light field, the competition between these lasing modes is discussed.     

Restoring reality for the self-dual N = 2 string

It is known that the critical N = (2,2) string describes 2 + 2 dimensional self-dual gravity in a non-covariant form, since it requires the choice of a complex structure in the target, which leaves only U(1,1) Lorentz symmetry. We briefly review picture-changing and spectral flow and show that the world-sheet Maxwell instantons individually break the Lorentz group further to SU(1,1). However, their contributions conspire to restore full SO(2,2) global symmetry if dilaton and axion fields are assembled in a null anti-self-dual two-form, denying them the status of Lorentz scalars. We present the fullySO (2,2) invariant tree-level three-point amplitude and the corresponding extension of the Plebanski action for self-dual gravity.     

Towards Optimal Disorder in Gold Nanosponges for Long‐Lived Localized Plasmonic Modes

The potential of disorder to confine and enhance electromagnetic fields is well known and localized fields in turn can be used for non‐linear optical sensing and for studying quantum optics. Recently, nanoporous gold nanoparticles (nanosponges) were shown to support highly localized long‐lived plasmonic modes in the infrared spectral range. In this paper, we take first steps towards tailoring the disorder for optimal field localization and enhancement by calculating extinction and near‐field properties for different filling fractions and correlation lengths. We find that the filling fraction has not only a large effect on the fundamental dipolar surface‐plasmon resonance of the nanoparticle, but also on the frequency range in which localized modes of plasmonic nature occur. The influence of the correlation length is more subtle but is seen to influence the coupling between localized and far‐field modes as well. We briefly discuss first results on details of the localization process, which takes place on the same length scale as the typical structure size, so a simple cavity‐resonance picture cannot account for the relatively low frequency of the modes.