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

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References

SHOWING 1-10 OF 39 REFERENCES
BRST symmetry of doubled membrane sigma-models
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 recentExpand
Double field theory and membrane sigma-models
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 anExpand
Bootstrapping non-commutative gauge theories from L∞ algebras
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 notExpand
Sigma models for genuinely non-geometric backgrounds
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 modelExpand
Non-geometric Backgrounds and the First Order String Sigma Model
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 theExpand
Manin Triples for Lie Bialgebroids
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 doesExpand
On the structure of graded symplectic supermanifolds and Courant algebroids
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 bundlesExpand
The Geometry of the Master Equation and Topological Quantum Field Theory
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
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 CourantExpand
$L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
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. InExpand
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