Related papers: Spinors as automorphisms of the tangent bundle
It is well-known that topological sigma-models in 2 dimensions constitute a path-integral approach to the study of holomorphic maps from a Riemann surface S to an almost complex manifold K, the most interesting case being that where K is a…
Given a $\mathbb Z_2$-harmonic spinor satisfying some genericity assumptions, this article constructs a 1-parameter family of two-spinor Seiberg-Witten monopoles converging to it after renormalization. The proof is a gluing construction…
It has been argued recently that mirror symmetry exchanges two pure spinors characterizing a generic manifold with SU(3)-structure. We show how pure spinors are modified in the presence of topological D-branes, so that they are still…
The pure spinor formulation of superstring theory includes an interacting sector of central charge $c_{\lambda}=22$, which can be realized as a curved $\beta\gamma$ system on the cone over the orthogonal Grassmannian $\text{OG}^{+}(5,10)$.…
Four-dimensional supersymmetric type II string theory vacua can be described elegantly in terms of pure spinors on the generalized tangent bundle T+T*. In this paper, we apply the same techniques to any ten-dimensional supersymmetric…
A review of some facts concerning classical spacetime geometry is presented together with a description of the most elementary aspects of the two-component spinor formalisms of Infeld and van der Waerden. Special attention is concentrated…
A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and…
Exploring the concept of the extended Galilei group $\mathcal{G}$, a representation for the symplectic quantum mechanics in the manifold of $\mathcal{G}$, written in the light-cone of a five-dimensional De Sitter space-time, is derived…
We construct N=2 supersymmetric nonlinear sigma models whose target spaces are tangent as well as cotangent bundles over the quadric surface Q^{n-2} = SO(n)/[SO(n-2)\times U(1)]. We use the projective superspace framework, which is an…
Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains…
We rewrite the N=(2,2) non-linear sigma model using auxiliary spinorial superfields defining the model on ${\cal T}\oplus^ *{\cal T}$, where ${\cal T}$ is the tangent bundle of the target space. This is motivated by possible connections to…
We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular…
We explicitly construct a symplectomorphism that relates magnetic twists to the invariant hyperk\"ahler structure of the tangent bundle of a Hermitian symmetric space. This symplectomorphism reveals foliations by (pseudo-) holomorphic…
We define the quasi-compact Higgs $G^{\mathbb C}$-bundles over singular curves introduced in our previous paper for the Lie group SL($N$). The quasi-compact structure means that the automorphism groups of the bundles are reduced to the…
We consider Riemannian 4-manifolds $(X,g_X)$ with a Spin^c-structure and a suitable circle bundle $Y$ over $X$ such that the Spin^c-structure on $X$ lifts to a spin structure on $Y$. With respect to these structures a spinor $\phi$ on $X$…
We investigate the geometry of holomorphic vector bundles $E$ over a Riemann surface $C$ together with a section of the endomorphism bundle tensored with $K^{1/2}$ -- a square root of the canonical bundle $K$. These parallel to some extent…
The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string, and the Kodaira-Spencer theory for the closed…
We introduce a simple lattice spin model that is written in terms of the well-known four-dimensional $\gamma$-matrix representation of the Clifford algebra. The local spins with a four-dimensional Hilbert space transform in a spinorial…
Kazama has described an extension of the N=2 superconformal algebra in which the operator product of G^- with itself is singular. In this paper, we relate actions of this chiral algebra to Drinfeld's theory of Manin pairs, or equivalently,…
This article announces a series of articles aiming at introducing the concept of symplectic spinors into symplectic topology resp. the concept of Frobenius structures. We will give lower bounds for the number of fixed points of a…