Related papers: Exotic Courant algebroids and T-duality
A duality theory of bundles of C$^*$-algebras whose fibres are twisted transformation group algebras is established. Classical T-duality is obtained as a special case, where all fibres are commutative tori, i.e. untwisted group algebras for…
A non-Abelian analogue of the Abelian T-duality momentum-winding exchange is described. The non-Abelian T-duality relates $\sigma$-models living on the cosets of a Drinfeld double with respect to its isotropic subgroups. The role of the…
Exotic duality suggests a link between gauge theories for differential p-forms and tensor fields of mixed symmetry [D-2,p] in D spacetime dimensions. On the other hand, standard Hodge duality relates p-form to (D-p-2)-form gauge potentials…
We introduce M-theoretic generalisations of the notion of (exact) Courant algebroid, and summarise their connections to generalised geometry, U-duality, and the physics of strings, membranes, and fivebranes. This is a summary of a paper…
We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan…
Darboux theorem in symplectic geometry is the crux of emergent gravity in which the gravitational metric emerges from a noncommutative U(1)-theory. Topological T-duality, on the other hand, is a relation between two a priori different…
In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find the bialgebras which are in duality with…
We extend the notion of T-duality to manifolds endowed with non-principal torus actions. The singularities of the torus action are controlled by a certain Lie algebroid, called the elliptic tangent bundle. Using this Lie algebroid, we…
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
String-theoretic T-duality can be exploited to simplify some features of the bulk-boundary correspondence in condensed matter theory. This paper surveys how T-duality links position and momentum space pictures of that correspondence.
We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result…
We consider the symmetries of a closed bosonic string, starting with the general coordinate transformations. Their generator takes vector components $\xi^\mu$ as its parameter and its Poisson bracket algebra gives rise to the Lie bracket of…
We use noncommutative topology to study T-duality for principal torus bundles with H-flux. We characterize precisely when there is a "classical" T-dual, i.e., a dual bundle with dual H-flux, and when the T-dual must be "non-classical," that…
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
We generalize Hansen--Strobl's definition of $H$-twisted Courant algebroid such that the twist $H$ of the Jacobi identity is a 4-form in the kernel of the anchor map and is closed under a naturally occurring exterior covariant derivative.…
In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant algebroids to generalize the notion of the…
We provide a short review of Courant algebroids and graded symplectic manifolds and show how different Courant algebroids emerge from double field theory. Fluxes of double field theory and their Bianchi identities are formulated by using…
Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of…
Open descendants with boundaries and crosscaps of non-trivial automorphism type are studied. We focus on the case where the bulk symmetry is broken to a Z_2 orbifold subalgebra. By requiring positivity and integrality for the open sector,…