scholarly journals Exotic Courant algebroids and T-duality

2021 ◽  
Vol 163 ◽  
pp. 104155
Author(s):  
Jaklyn Crilly ◽  
Varghese Mathai
Keyword(s):  
Courant Algebroids

scholarly journals Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Grgur Šimunić
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Target Space ◽  
Two Dimensional ◽  
Courant Algebroids ◽  
Dirac Structures ◽  
Courant Algebroid ◽  
Abelian Case ◽  
Jacobi Manifolds ◽  
Jacobi Structure

Abstract We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the Abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-Abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.

scholarly journals Leibniz 2-Algebras and Twisted Courant Algebroids

2013 ◽  
Vol 41 (5) ◽  
pp. 1929-1953 ◽  
Author(s):  
Yunhe Sheng ◽  
Zhangju Liu
Keyword(s):  
Courant Algebroids

scholarly journals Hypercomplex structures on Courant algebroids

2009 ◽  
Vol 347 (9-10) ◽  
pp. 545-550 ◽  
Author(s):  
Mathieu Stiénon
Keyword(s):  
Courant Algebroids

scholarly journals Split Courant algebroids as L∞-structures

2020 ◽  
Vol 155 ◽  
pp. 103790
Author(s):  
P. Antunes ◽  
J.M. Nunes da Costa
Keyword(s):  
Courant Algebroids

2-PLECTIC MANIFOLDS AND ITS RELATION WITH COURANT ALGEBROIDS

2012 ◽  
Vol 09 (03) ◽  
pp. 1250015
Author(s):  
M. SHAFIEE
Keyword(s):  
Lie Group ◽  
Lagrangian Submanifolds ◽  
Compact Lie Group ◽  
Courant Algebroids ◽  
Courant Algebroid ◽  
Hamiltonian Group

In this paper we study the relation between 2-plectic manifolds and Courant algebroids. We establish a relation between 2-Lagrangian submanifolds of 2-plectic manifolds and subbundles of Courant algebroids. Also we show that an action of a compact Lie group G on a 2-plectic manifold (M, ω) can be extended to an action of G on an exact Courant algebroid E over M if and only if G is a subgroup of Hamiltonian group of (M, ω).

scholarly journals Pre-Courant algebroids

2019 ◽  
Vol 142 ◽  
pp. 254-273 ◽  
Author(s):  
Andrew James Bruce ◽  
Janusz Grabowski
Keyword(s):  
Courant Algebroids
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