Bascone, Francesco (2022) Dualities and geometrical aspects of sigma models. [Tesi di dottorato]

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Abstract

The concept of duality is of fundamental importance in theoretical physics, and it refers to the existence of different descriptions of the same physical phenomenon in a different mathematical language. One particularly important application for dualities is string theory, relating string theories defined on different spacetimes. Another fundamental concept is that of sigma model, which is also necessary to describe strings propagating on the spacetime. This thesis is based on the elaboration and application of a novel approach to the so-called Poisson-Lie T-duality. In particular, the approach is based on deforming the underlying current algebra involved in sigma models having Poisson-Lie dual groups as target spaces. This leads to the formulation of new families of dual models, all related by particular T-duality transformations. This approach is expected to give rise to new theories, and it is particularly well suited for formal quantization based on quantum groups. Looking for generalizations of this framework we have defined a sigma model having a Jacobi manifold as target space, and for this reason we called it Jacobi sigma model, as a generalization of the so-called Poisson sigma model. The Poisson sigma model on Lie groups with Poisson structure seems to lead naturally to the concept of Poisson-Lie duality, and one of the goals of the thesis is to include such duality aspects into the newly defined Jacobi sigma model. Other than duality aspects, the Jacobi sigma model can take new string solutions into account (with fluxes in particular), which is not possible to obtain from the Poisson sigma model.

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