  This thesis follows two main lines of research, both related to relevant
aspects of string theory and its phenomenological/cosmological applications. We
study two different generalizations of the integrable SG model to NC geometry,
after discussing general properties and issues of integrable theories and NC
field theories, mentioning their role in string theory. The question is whether
we can obtain an integrable NC SG with factorized S matrix. Of the two models
we study, the second NC SG -- derived by dimensional reduction from the stringy
NC self-dual YM in (2+2) dimensions -- exhibits the good properties of S matrix
required by integrability in 2D, while the first one does not. As a second
topic, a particular brane-world model is analyzed both from the cosmological
point of view and in the spirit of holography, after introducing conventional
cosmology, brane-worlds and AdS/CFT. The 7D RS set-up with brane-bulk energy
exchange we propose leads to a non conventional cosmological evolution where
all fixed points have positive acceleration and are found to be stable for a
wide range of choices for the parameters. We construct the holographic dual
theory, represented by a renormalized 6D CFT coupled to 6D gravity. The
matching of parameters on the two sides of the duality is then achieved in
specific approximations.
