Related papers: Transverse generalized metrics and 2d sigma models
We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we…
In this paper, we develop the mathematical formulation of metric string structures. These play a crucial role in the formulation of certain six-dimensional superconformal field theories and we believe that they also underlie potential…
We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on a Cartan geometry. We prove that there is a bijection…
This is a survey article on a known generalization of Dirac-type operators to transverse operators called basic Dirac operators on Riemannian foliations, which are smooth foliations that have a transverse geometric structure. Construction…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
We characterize the Dirac structures that are parallel with respect to Gualtieri's canonical connection of a generalized Riemannian metric. On the other hand, we discuss Dirac structures that are images of generalized tangent structures.…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We study the new ``gauge'' theories in 5+1 dimensions, and their non-commutative generalizations. We argue that the $\theta$-term and the non-commutative torus parameters appear on an equal footing in the non-critical string theories which…
Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We…
We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over…
The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class…
We discuss two classes of exact (in $\a'$) string solutions described by conformal sigma models. They can be viewed as two possibilities of constructing a conformal model out of the non-conformal one based on the metric of a $D$-dimensional…
Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of…
It has been known for a while that the effective geometrical description of compactified strings on $d$-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized…
We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge non invariant quantity. This generalizes the R <--> 1/R symmetry in which momenta and…