Twisted Vector Research Articles

Semi-stable twisted holomorphic vector bundles over Gauduchon manifolds

In this paper, we study the semi-stable twisted holomorphic vector bundles over compact Gauduchon manifolds. By using Uhlenbeck–Yau's continuity method, we show that the existence of approximate Hermitian–Einstein structure and the semi-stability of twisted holomorphic vector bundles are equivalent over compact Gauduchon manifolds. As its application, we show that the Bogomolov type inequality is also valid for a semi-stable twisted holomorphic vector bundle.

NORMALISED TANGENT BUNDLE, VARIETIES WITH SMALL CODEGREE AND PSEUDOEFFECTIVE THRESHOLD

AbstractWe propose a conjectural list of Fano manifolds of Picard number $1$ with pseudoeffective normalised tangent bundles, which we prove in various situations by relating it to the complete divisibility conjecture of Francesco Russo and Fyodor L. Zak on varieties with small codegree. Furthermore, the pseudoeffective thresholds and, hence, the pseudoeffective cones of the projectivised tangent bundles of rational homogeneous spaces of Picard number $1$ are explicitly determined by studying the total dual variety of minimal rational tangents (VMRTs) and the geometry of stratified Mukai flops. As a by-product, we obtain sharp vanishing theorems on the global twisted symmetric holomorphic vector fields on rational homogeneous spaces of Picard number $1$ .

Kobayashi—Hitchin correspondence for twisted vector bundles

Abstract We prove the Kobayashi—Hitchin correspondence and the approximate Kobayashi—Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a compact manifold and g is a Gauduchon metric on X, a twisted holomorphic vector bundle on X is g−polystable if and only if it is g−Hermite-Einstein, and if X is a compact Kähler manifold and g is a Kähler metric on X, then a twisted holomorphic vector bundle on X is g−semistable if and only if it is approximate g−Hermite-Einstein.

EVIDENCE FOR HIGHLY RELATIVISTIC VELOCITIES IN THE KILOPARSEC-SCALE JET OF THE QUASAR 3C 345

In this paper we use radio polarimetric observations of the jet of the nearby bright quasar 3C\,345 to estimate the fluid velocity on kiloparsec scales. The jet is highly polarized, and surprisingly, the electric vector position angles in the jet are ``twisted'' with respect to the jet axis. Simple models of magnetized jets are investigated in order to study various possible origins of the electric vector distribution. In a cylindrically-symmetric transparent jet a helical magnetic field will appear either transverse or longitudinal due to partial cancellations of Stokes parameters between the front and back of the jet. Synchrotron opacity can break the symmetry, but it leads to fractional polarization less than that observed, and to strong frequency dependence that is not seen. Modeling shows that differential Doppler boosting in a diverging jet can break the symmetry, allowing a helical magnetic field to produce a twisted electric vector pattern. Constraints on the jet inclination, magnetic field properties, intrinsic opening angle, and fluid velocities are obtained, and show that highly relativistic speeds ($\beta \ga 0.95$) are required. This is consistent with the observed jet opening angle, with the absence of a counter-jet, with the polarization of the knots at the end of the jet, and with some inverse-Compton models for the X-ray emission from the 3C\,345 jet. This model can also apply on parsec scales and may help explain those sources where the electric vector position angles in the jet are neither parallel nor transverse to the jet axis.

Twisted vector field from an inhomogeneous and anisotropic metamaterial

We propose a metamaterial design for realizing inhomogeneous and anisotropic effective media based on the localized waveguide resonance mechanism. Such a design can be easily achieved in experiment and enables us to simultaneously manipulate the wavefront and the state of polarization of the transmitted electromagnetic field by the polarization-sensitive extraordinary optical transmission. Numerical simulations, including the generation of the hybridized vector fields (especially twisted vector fields that are azimuthally polarized carrying a helical phase), prove the feasibility of our proposal. It could be expected as a good candidate of the specially designed subwavelength element for creating the exotic vector fields beyond the functionality of the existing vector fields in a wide spectral regime, especially the terahertz and radio regimes.

On a NAHE variation

We present a variation of the NAHE-basis for free fermionic heterotic string models. By rotating some of the boundary conditions of the NAHE periodic/anti-periodic fermions { y m , y ¯ m , w m , w ¯ m } , for m = 1 to 6, associated with the six compact dimensions of a bosonic lattice/orbifold model, we show an additional method for enhancing the standard NAHE gauge group of SO ( 10 ) back to E 6 . This rotation transforms ( SO ( 10 ) ⊗ SO ( 6 ) 3 ) obs ⊗ ( E 8 ) hid into ( E 6 ⊗ U ( 1 ) 5 ) obs ⊗ SO ( 22 ) hid . When SO ( 10 ) is enhanced to E 6 in this manner, the ith MSSM matter generation in the SO ( 10 ) 16 i rep, originating in the twisted basis vector b i , recombines with both its associated untwisted MSSM Higgs in a 10 i rep and an untwisted non-Abelian singlet ϕ i , to form a 27 i rep of E 6 . Beginning instead with the E 6 model, the inverse transformation of the fermion boundary conditions corresponds to partial GUT breaking via boundary rotation. Correspondence between free fermionic models with Z 2 ⊗ Z 2 twist (especially of the NAHE class) and orbifold models with a similar twist has received further attention recently. Our NAHE variation also involves a Z 2 ⊗ Z 2 twist and offers additional understanding regarding the free fermion/orbifold correspondence. Further, models based on this NAHE variation offer some different phenomenological features compared to NAHE-based models. In particular, the more compact Z 2 ⊗ Z 2 twist of the NAHE variation offers a range of mirror models not possible from NAHE-based models. Examples of such models are presented.

Modules over twisted group rings and vector bundles over the anisotropic real conic

We prove, in an elementary way, that a locally free sheaf of finite rank over the anisotropic real conic is the direct sum of indecomposable locally free sheaves of rank 1 or 2. Our proof is purely algebraic, and is based on a classification of graded ℂ[X, Y]-modules endowed with a certain action of the cyclic group ℤ/4ℤ.

Lagrangian Subcategories and Braided Tensor Equivalences of Twisted Quantum Doubles of Finite Groups

We classify Lagrangian subcategories of the representation category of a twisted quantum double D ω (G), where G is a finite group and ω is a 3-cocycle on it. In view of results of [DGNO] this gives a complete description of all braided tensor equivalent pairs of twisted quantum doubles of finite groups. We also establish a canonical bijection between Lagrangian subcategories of Rep(D ω (G)) and module categories over the category $${\rm Vec}_{G} ^{\omega}$$ of twisted G-graded vector spaces such that the dual tensor category is pointed. This can be viewed as a quantum version of V. Drinfeld’s characterization of homogeneous spaces of a Poisson-Lie group in terms of Lagrangian subalgebras of the double of its Lie bialgebra [D]. As a consequence, we obtain that two group-theoretical fusion categories are weakly Morita equivalent if and only if their centers are equivalent as braided tensor categories.

D= 2, 𝒩 = (2, 2) semi chiral vector multiplet

We describe a new 1+1 dimensional N=(2,2) vector multiplet that naturally couples to semi chiral superfields in the sense that the gauged supercovariant derivative algebra is only consistent with imposing covariantly semi chiral superfield constraints. It has the advantages that its prepotentials shift by semi chiral superfields under gauge transformations. We also see that the multiplet relates the chiral vector multiplet with the twisted chiral vector multiplet by reducing to either multiplet under appropriate limits without being reducible in terms of the chiral and twisted chiral vector multiplet. This is explained from the superspace geometrical point of view as the result of possessing a symmetry under the discrete supercoordinate transformation that is responsible for mirror copies of supermultiplets. We then describe how to gauge a non linear sigma model with semi chiral superfields using the prepotentials of the new multiplet.

Formula omitted] twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

We propose a N = 4 twisted superspace formalism in four dimensions by introducing a Dirac–Kähler twist. In addition to the BRST charge as a scalar counter part of the twisted supercharge we find vector and tensor twisted supercharges. By introducing twisted chiral superfields we explicitly construct an off-shell twisted N = 4 SUSY invariant action. We propose a variety of supergauge invariant actions by introducing twisted vector superfields. We may, however, need to find further constraints in order to identify a twisted N = 4 super-Yang–Mills action. We propose a superconnection formalism for the twisted superspace and constraints play a crucial role in the construction. It turns out that the N = 4 superalgebras obtained by a Dirac–Kähler twist can be decomposed into N = 2 sectors. We then construct twisted N = 2 super-Yang–Mills actions using this formalism in two and four dimensions.

Twisted vector bundles on pointed nodal curves

Motivated by the quest for a good compactification of the moduli space ofG-bundles on a nodal curve we establish a striking relationship between Abramovich’s and Vistoli’s twisted bundles and Gieseker vector bundles.

Une caractérisation des surfaces d'Inoue-Hirzebruch

We show that among the surfaces of class VII 0 with b 2 >0, the Inoue-Hirzebruch surfaces are characterized by the property of admitting two twisted vector fields. This result is a step towards the understanding of foliations on VII 0 surfaces.

Constraints on arm position when pointing in three dimensions: Donders' law and the Fick gimbal strategy.

1. While making saccades between targets with the head stationary, eye positions are constrained to two of the possible three degrees of freedom. Classically this constraint has been described by Donders' and Listing's laws. The objective was to determine whether these laws also apply for the straight arm when pointing between different targets. Thus we determined whether the arm adopts only one angular position for every pointing direction (Donders' law) and whether these positions can be described by rotations from a reference position about axes that lie in a plane (Listing's law). 2. The angular positions (orientations) of the arm in three-dimensional space were studied as subjects pointed with a straight arm at different targets. Arm position was measured with the search coil technique by means of coils attached to the back of the hand. Pointing was studied over a range of +/- 45 degrees in all directions from a central target located 45 degrees to the right of the straight-ahead position. 3. The positions of the arm in space were described by quaternion vectors, i.e., a particular position was described in terms of the axis and amplitude of a rotation from a reference position to that position. Using this description, it was found that the straight arm adopted a similar orientation (standard deviations ranged from 2.8 to 4.8 degrees) when pointing at a particular target irrespective of which target from which it had moved. 4. The angular position vectors for arm positions associated with relatively small movements (e.g., less than +/- 30 degrees) lay in a flat surface with minimal torsion. At first sight, this surface appeared to be similar to Listing's plane of the eye. However, for positions associated with larger movements (e.g., +/- 45 degrees) it became apparent that, unlike the eye, the surface deviated from one obeying Listing's law, i.e., it was twisted and showed torsion like that produced by rotations around the horizontal and vertical axes of a Fick gimbal. (The characteristic of a Fick gimbal is that the vertical axis is fixed, whereas the horizontal axis moves with the gimbal.) 5. Although there were differences between subjects, all showed a twisted position vector surface. The twist was always in the same direction, and it was always less than that of a Fick gimbal. 6. This position vector surface had a similar shape whether the arm was stationary or was moving between targets, whether subjects pointed with or without vision, and whether the pointing arm had moved between targets or from a bent-elbow position on the lap.(ABSTRACT TRUNCATED AT 400 WORDS)