相关论文: A Cartan tale of the orbifold superstring

The effective Hamiltonians for chiral supersymmetric gauge theories at small spatial volume are generalizations of the Hamiltonians describing the motion of a scalar or a spinor particle in a field of Dirac monopoles (we are dealing in fact…

Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the…

A rigid framework for the Cartan calculus of Lie derivatives, inner derivations, functions, and forms is proposed. The construction employs a semi-direct product of two graded Hopf algebras, the respective super-extensions of the deformed…

We present a modern formulation of \'Elie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system. The paper is divided into three parts. In part one, using notions…

We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of…

We study properties and the structure of Cartan subgroups in a connected Lie group. We obtain a characterisation of Cartan subgroups which generalises W\"ustner's structure theorem for the same. We show that Cartan subgroups are same as…

An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational…

We review a geometrical, so called superembedding, approach to the description of the dynamics of point-like and extended supersymmetric objects (superbranes) in String Theory. The approach is based on a supersymmetric extension of the…

This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles (E\to M_{0}) by canonically associating…

We prove that the prescription for construction of supersymmetric lattice gauge theories by orbifolding and deconstruction directly leads to Catterall's geometrical discretization scheme in general. These two prescriptions always give the…

By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs…

In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. We introduce equivariant cohomology and equivariant formal deformation theory of Lie superalgebras. As an application of equivariant…

Let $\Omega$ be the {\em superspace ring} of polynomial-valued differential forms on affine $n$-space. The natural action of the symmetric group $\mathfrak{S}_n$ on $n$-space induces an action of $\mathfrak{S}_n$ on $\Omega$. The {\em…

Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them…

A formalism is presented to construct a non-perturbative Grand Unified Theory when gravitational Planck-scale phenomena are included. The fundamental object on the Planck scale is the three-torus T^3 from which the known properties of…

Over algebraically closed fields of characteristic p>2, prolongations of the simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. Several new simple Lie…

We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…

We analyze the superstring propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear sigma-model and the structure of rational curves on the Calabi-Yau manifold. We study in…

We show that the maximal orbit dimension of a simultaneous Lie group action on n copies of a manifold does not pseudo-stabilize when n increases. We also show that if a Lie group action is (locally) effective on subsets of a manifold, then…

Recent work applying higher gauge theory to the superstring has indicated the presence of `higher symmetry'. Infinitesimally, this is realized by a `Lie 2-superalgebra' extending the Poincare superalgebra in precisely the dimensions where…