Born sigma-models for para-Hermitian manifolds and generalized T-duality

@article{Marotta2021BornSF,
  title={Born sigma-models for para-Hermitian manifolds and generalized T-duality},
  author={Vince Marotta and Richard J Szabo},
  journal={Reviews in Mathematical Physics},
  year={2021}
}
We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely defines a worldsheet sigma-model with a para-Hermitian target space, and we describe its Lie algebroid gauging as a means of recovering the conventional sigma-model description of 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

Born sigma model for branes in exceptional geometry

In double field theory, the physical space has been understood as a subspace of the doubled space. Recently, the doubled space has been defined as the para-Hermitian manifold and the physical space

D-Branes in Para-Hermitian Geometries

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

Algebroids, AKSZ Constructions and Doubled Geometry

Abstract We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their

Complex structures, T-duality and worldsheet instantons in Born sigma models

Abstract We investigate doubled (generalized) complex structures in 2D-dimensional Born geometries where T-duality symmetry is manifestly realized. We show that Kähler, hyperkähler, bi-hermitian and

Gauged sigma models and exceptional dressing cosets

The Poisson–Lie (PL) T-duality is a generalized T-duality based on the Lie algebra of the Drinfel’d double. In particular, when we consider the PL T-duality of a coset space, the dual space is

A QP perspective on topology change in Poisson-Lie T-duality

We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QPmanifold on

Currents, charges and algebras in exceptional generalised geometry

A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of halfBPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It

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

References

SHOWING 1-10 OF 117 REFERENCES

Lie algebroids, gauge theories, and compatible geometrical structures

The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge

Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T -duality

A bstractBased on the construction of Poisson-Lie T -dual σ-models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T -duality group. This group

A geometry for non-geometric string backgrounds

A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to

Gauging without initial symmetry

A Unique Connection for Born Geometry

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

Lie Algebroids, Holonomy and Characteristic Classes

Abstract We extend the notion of connection in order to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual

New supersymmetric string compactifications

We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non Calabi-Yau spaces in the

Poisson Geometry with a 3-Form Background

We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable

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,

Doubled geometry and T-folds

The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological
...