• Corpus ID: 121421651

# M ar 2 01 2 On the geometry of double field theory by Izu Vaisman

@inproceedings{2013MA2,
title={M ar 2 01 2 On the geometry of double field theory by Izu Vaisman},
author={},
year={2013}
}
• Published 2013
• Mathematics
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 paraKähler manifolds. We define metric algebroids, which are vector bundles with a bracket of cross sections that has the same metric compatibility property as a Courant bracket. We show that a double field gives rise to two canonical connections, whose scalar curvatures can be…

### Double field theory, twistors, and integrability in 4-manifolds

The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory,

### Global aspects of doubled geometry and pre-rackoid

• Mathematics
• 2020
The integration problem of a C-bracket and a Vaisman (metric, pre-DFT) algebroid which are geometric structures of double field theory (DFT) is analyzed. We introduce a notion of a pre-rackoid as a

### Metric algebroid and Dirac generating operator in Double Field Theory

• Mathematics
• 2020
We give a formulation of Double Field Theory (DFT) based on a metric algebroid. We derive a covariant completion of the Bianchi identities, i.e. the pre-Bianchi identity in torsion and an improved

### D-Branes in Para-Hermitian Geometries

• Mathematics
Universe
• 2022
We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal

### Towards an extended/higher correspondence

Abstract In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes. Double Field Theory is

### Double field theory algebroid and curved L∞-algebras

• Mathematics
• 2021
A double field theory algebroid (DFT algebroid) is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory. In particular, a

### The Puzzle of Global Double Field Theory: Open Problems and the Case for a Higher Kaluza‐Klein Perspective

The history of the geometry of Double Field Theory is the history of string theorists' effort to tame higher geometric structures. In this spirit, the first part of this paper will contain a brief

### DFT algebroid and curved $L_\infty$-algebras

• Mathematics
• 2020
A DFT algebroid is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory. In particular, a DFT algebroid is a structure

### Global Double Field Theory is Higher Kaluza‐Klein Theory

Kaluza‐Klein Theory states that a metric on the total space of a principal bundle P→M , if it is invariant under the principal action of P, naturally reduces to a metric together with a gauge field

### Proposal of a questionnaire to measure the level of interaction in the university classrooms: version for teachers, students and observers

• Education
WPOM-Working Papers on Operations Management
• 2019
Throughout the literature, there are several studies that highlight the importance of interaction in the classroom as a means to promote student learning. Based on this idea, and due to the absence

## References

SHOWING 1-10 OF 21 REFERENCES

### Differential geometry with a projection: application to double field theory

• Mathematics
• 2011
In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is

### The Gauge algebra of double field theory and Courant brackets

• Physics, Mathematics
• 2009
We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are

### Generalized Calabi-Yau manifolds

A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi–Yau manifold and also a symplectic manifold. Such structures are of either odd or even type

### Frame-like geometry of double field theory

• Mathematics
• 2011
We relate two formulations of the recently constructed double field theory to a frame-like geometrical formalism developed by Siegel. A self-contained presentation of this formalism is given,

### Generalized metric formulation of double field theory

• Mathematics
• 2010
The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled

### Manin Triples for Lie Bialgebroids

• Mathematics
• 1995
In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does

### Homogeneous para-Kähler Einstein manifolds

• Mathematics
• 2009
A para-Kahler manifold can be defined as a pseudo-Riemannian manifold with a parallel skew-symmetric para-complex structure , that is, a parallel field of skew-symmetric endomorphisms with or,

### Stringy differential geometry, beyond Riemann

• Physics
• 2011
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we

### Generalized Complex Geometry

Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group,