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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.

We build on the results of [1] for generalised frame fields on generalised quotient spaces and study integrable deformations for ℂPn. In particular we show how, when the target space of the Principal Chiral Model is a complex projective space, a two-parameter deformation can be introduced in principle. The second parameter can however be removed via a diffeomorphism, which we construct explicitly, in accordance with the results stemming from a thorough integrability analysis we carry out. We also elucidate how the deformed target space can be seen as an instance of generalised Kähler, or equivalently bi-Hermitian, geometry. In this respect, we find the generic form of the pure spinors for ℂPn and the explicit expression for the generalised Kähler potential for n = 1, 2.

Recent work has shown that two-dimensional non-linear $\sigma$-models on group manifolds with Poisson-Lie symmetry can be understood within generalised geometry as exemplars of generalised parallelisable spaces. Here we extend this idea to target spaces constructed as double cosets $M=\widetilde{G} \backslash D / H$. Mirroring conventional coset geometries, we show that on $M$ one can construct a generalised frame field and a $H$-valued generalised spin connection that together furnish an algebra under the generalised Lie derivative. This results naturally in a generalised covariant derivative with a (covariantly) constant generalised intrinsic torsion, lending itself to the construction of consistent truncations of 10-dimensional supergravity compactified on $M$. An important feature is that $M$ can admit distinguished points, around which the generalised tangent bundle should be augmented by localised vector multiplets. We illustrate these ideas with explicit examples of two-dimensional parafermionic theories and NS5-branes on a circle., Comment: 24 pages, Merry Christmas!

Speech is an important aspect of human communication; individuals with speech impairment are unable to communicate vocally in real time. Our team has developed the TongueToSpeech (TTS) device with the goal of augmenting speech communication for the vocally impaired. The proposed device is a wearable wireless assistive device that incorporates a capacitive touch keyboard interface embedded inside a discrete retainer. This device connects to a computer, tablet or a smartphone via Bluetooth connection. The developed TTS application converts text typed by the tongue into audible speech. Our studies have concluded that an 8-contact point configuration between the tongue and the TTS device would yield the best user precision and speed performance. On average using the TTS device inside the oral cavity takes 2.5 times longer than the pointer finger using a T9 (Text on 9 keys) keyboard configuration to type the same phrase. In conclusion, we have developed a discrete noninvasive wearable device that allows the vocally impaired individuals to communicate in real time.