Duality and Integrability in String Theory

This thesis investigates aspects of duality and integrable deformations in String Theory. In the first two chapters we review standard material in Mathematics and Physics, laying the ground to the novel contributions later reported. In Chapter 4 we introduce gener alised cosets, on which we are able to provide a canonical construction for a generalised frame field and spin connection that together furnish an algebra under the generalised Lie derivative. In Chapter 5 we study the geometric properties of the Yang-Baxter defor mation of CPn, showing that it constitutes an exemplar of Generalised Kähler Geometry. For CP2 we compute the generalised Kähler potential. Tangentially, we furnish a closed form for the metric and B-field of the Yang-Baxter deformed sphere Sn, for every n. In Chapter 7 we address the problem of two-loop renormalisation of the Tseytlin dou bled string for cosmological spacetimes. Whilst the results do satisfy a number of key consistency criteria, we find however that the two-loop counter-terms are incompatible with O(n, n) symmetry, pointing perhaps to the presence of scheme changes. In Chapter 8 we build on this work and set the stage for a two-loop calculation for a Poisson-Lie T-duality covariant theory