| Sažetak | In this thesis we study the interplay between topological sigma models and generalized geometry. Firstly, they are related through generalized gauging procedure by the notion of Lie algebroids replacing the more conventional situation of Lie algebras. Furthermore, the gauging of the 2-dimensional string models in the target space with the background metric g and a closed 3-form H is closely related to Dirac structures of exact Courant algebroids. Here we expand on this, firstly by showing that the coupling to the metric can only be minimal, and secondly by allowing the 3-form to be non-closed, a situation that arises in the context of heterotic strings. It is shown that this is again related to Dirac structures, but this time of transitive Courant algebroid. The gauged action obtained by gauging the 2-dimensional string model is related to Dirac sigma models, which as the special case contains twisted Poisson sigma model (TPSM). Thus, Dirac sigma models can be considered as a generalization of the TPSM. Another such generalization is introduced here in the form of Jacobi sigma model, a new 2-dimensional sigma model. Geometrically, this corresponds to Jacobi structures which can be considered as a generalization of Poisson structures to which the Poisson sigma model corresponds. The final generalization of TPSM of relevance here is that of (twisted) R-Poisson sigma model which, unlike the previously mentioned Dirac and Jacobi sigma models, is a higher dimensional one. This sigma model corresponds to R-Poisson structures, which adds an additional multibracket to the Poisson bracket of the Poisson manifolds. Finally, the classical BV action has been constructed for the above sigma models as a first step towards their quantization. The significance of this result is that, despite being topological field theories, their BV action cannot be obtained through the AKSZ construction due to the absence of the QP-structure on the target space, thus requiring different methods for the constructions of the BV action. Thus, the methods used here lead to the classical BV action for two significant theories (Dirac and R-Poisson sigma models), but also directly show different strategies for the construction of the BV action when more convenient methods are not available. Keywords: Sigma models, Gauging procedure, Lie algebroids, Courant algebroids, Dirac sigma model, Jacobi sigma model, Batalin-Vilkovisky formalism |
