arXiv research

The paper reviews a correspondence between Double Field Theory and bundle gerbes.

Survey of global geometry for double field theory.

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangen…

Defines the algebroid structure of double field theory.

Extends Double Field Theory with new kinematical structure.

Study topological A/B-models using double field theory and generalized geometry.

Characterizes a specific type of Courant algebroid with a Calabi-Yau structure.

Double field theory was developed by theoretical physicists as a way to encompass $T$-duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms, in the framework of para-Kaehler manifolds. We define metric algebroids, which are vector bundles with a bracket of cross se…

In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes finite transformation law highly complicated, both technically and conceptually. In…

This work applies Double Field Theory to four-dimensional manifolds, revealing connections to integrability and twistor theory.

Global Double Field Theory is a higher-dimensional generalization of Kaluza-Klein theory.

Vaisman algebroid explains gauge symmetry in DFT.

Extended Riemannian geometry aids in DFT formulations.

A new discretisation of a doubled, i.e. BF, version of the pure abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely the partition function and correlation function of Wilson loops. Similarities with free spinor field theory a…

Investigates geometric aspects of double field theory and its membrane sigma-model formulation.

Integrates C-bracket and Vaisman algebroid structures in double field theory.

Program connects quantum computing and topological field theories.

Survey para-Hermitian geometry and its applications in physics.

Double Lie algebroids were discovered by Kirill Mackenzie from the study of double Lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for Lie algebroids and double vector bundles. In this paper we establish a simple alternative characterization of double Lie algebroids…

Observable structures of a topological field theory of AKSZ type are analyzed. From a double (or multiple) complex structure of observable algebras, new topological invariants are constructed. Especially, Donaldson polynomial invariants and their generalizations are constructed from a topological field theory of AKSZ t…

We give a simple characterization of Mackenzie's double Lie algebroids in terms of homological vector fields. Application to the `Drinfeld double' of Lie bialgebroids is given and an extension to the multiple case is suggested.

A new method analyzes topological B-model on a torus using doubled geometry.

Generalizes graded bundles with more flexible transformation laws.

This text is meant to be a brief overview of the topics announced in the title and is based on my talk in Vienna (August/September 2007). It does not contain new results (except probably for a remark concerning Q-manifold homology, which I wish to elaborate elsewhere). "Mackenzie theory" stands for the rich circle of n…

We construct a C-space associated with every closed 3-form on a spacetime $M$ and show that it depends on the class of the form in $H^3(M, Z)$. We also demonstrate that C-spaces have a relation to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and …

Unified description of fluxes and T-duality via symplectic manifolds.

Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking numbers respectively. The new feature which makes this possible is the introduction o…

Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of mot…

Enhances Hamiltonian systems stability through generalized double bracket vector fields.

Global construction of D-bracket from para-Hermitian manifolds.

Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} = *C$ independent of $B$ via the Hodge duality $*$. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of nonc…

The paper develops a theory linking Hamiltonian and quasi-Hamiltonian manifolds.

The paper explores the structure of double complexes and their applications.

Summary of para-Hermitian geometry for T-duality in string theory.

Proves a unique connection for Born geometry.

Motivated by generalized geometry, we discuss differential geometric structures on the total space $\mathfrak{T}M$ of the bundle $TM\oplus T^*M$, where $M$ is a differentiable manifold; $\mathfrak{T}M$ is called a big-tangent manifold. The vertical leaves of the bundle are para-Hermitian vector spaces. The big-tangent …

Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.

We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3-di…

On a Poisson manifold endowed with a Riemannian metric we will construct a vector field that generalizes the double bracket vector field defined on semi-simple Lie algebras. On a regular symplectic leaf we will construct a generalization of the normal metric such that the above vector field restricted to the symplectic…

This thesis proposes a global geometric formulation of Extended Field Theories.

We define a new algebra for double vector bundles, linking it to Lie algebroids.

We develop new algebraic methods refining the Witt group of linking forms and Ranicki's torsion algebraic L-groups into double Witt groups and double L-groups. At each prime ideal of the underlying ring, our double Witt groups capture infinitely many more integral signatures of the linking form than the single Witt gro…

Paper defines and proves geometric uniqueness of Einstein field equations.

A new algebraic structure extends Drinfel'd double for U-duality applications.

New approach connects 3D Chern-Simons theory to spectral networks.

The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important featu…

Proposes a topological framework to study modular invariants and related concepts.

Introduces Poisson double algebroids and their relation to Lie 2-bialgebras.