# Courant Sigma Model and ‐algebras

@article{Grewcoe2020CourantSM, title={Courant Sigma Model and ‐algebras}, author={C. J. Grewcoe and L. Jonke}, journal={arXiv: High Energy Physics - Theory}, year={2020} }

The Courant sigma model is a 3-dimensional topological sigma model of AKSZ type which has been used for the systematic description of closed strings in non-geometric flux backgrounds. In particular, the expression for the fluxes and their Bianchi identities coincide with the local form of the axioms of a Courant algebroid. On the other hand, the axioms of a Courant algebroid also coincide with the conditions for gauge invariance of the Courant sigma model. In this paper we embed this interplay… Expand

#### Tables from this paper

#### 7 Citations

L∞-algebras and membrane sigma models

- 2020

Membrane sigma-models have been used for the systematic description of closed strings in nongeometric flux backgrounds. In particular, the conditions for gauge invariance of the corresponding action… Expand

DFT algebroid and curved $L_\infty$-algebras

- Physics
- 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… Expand

The geometry, branes and applications of exceptional field theory

- Physics
- 2020

This is a review of exceptional field theory: a generalisation of Kaluza-Klein theory that unifies the metric and $p$-form gauge field degrees of freedom of supergravity into a generalised or… Expand

Algebroids, AKSZ Constructions and Doubled Geometry

- Physics, Mathematics
- 2021

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… Expand

Double field theory algebroid and curved L∞-algebras

- Physics, 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… Expand

Topological Field Theories induced by twisted R-Poisson structure in any dimension

- Physics, Mathematics
- 2021

We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions ≥ 2 whose target space has a geometrical structure that suitably generalizes Poisson or twisted… Expand

$L_\infty$-algebras and membrane sigma models

- Physics, Mathematics
- 2020

Membrane sigma-models have been used for the systematic description of closed strings in non-geometric flux backgrounds. In particular, the conditions for gauge invariance of the corresponding action… Expand

#### References

SHOWING 1-10 OF 39 REFERENCES

BRST symmetry of doubled membrane sigma-models

- Physics, Mathematics
- 2019

Courant sigma-models encode the geometric and non-geometric fluxes of compactified closed string theory as generalized Wess-Zumino terms and exhibit their relation to Courant algebroids. In recent… Expand

Double field theory and membrane sigma-models

- Physics, Mathematics
- 2018

A bstractWe investigate geometric aspects of double field theory (DFT) and its formulation as a doubled membrane sigma-model. Starting from the standard Courant algebroid over the phase space of an… Expand

Bootstrapping non-commutative gauge theories from L∞ algebras

- Physics, Mathematics
- 2018

A bstractNon-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not… Expand

Sigma models for genuinely non-geometric backgrounds

- Physics
- 2015

A bstractThe 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… Expand

Non-geometric Backgrounds and the First Order String Sigma Model

- Physics
- 2009

We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bi-vector, a two-form and an inverse metric. Lifting the… Expand

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… Expand

On the structure of graded symplectic supermanifolds and Courant algebroids

- Mathematics, Physics
- 2002

This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles… Expand

The Geometry of the Master Equation and Topological Quantum Field Theory

- Physics
- 1997

In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold,… Expand

Membrane sigma-models and quantization of non-geometric flux backgrounds

- Physics, Mathematics
- 2012

A bstractWe develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M . Starting from a suitable Courant… Expand

$L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism

- Physics, Mathematics
- 2018

We review in detail the Batalin-Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In… Expand