Fermionic variations on AdS/CFT themes

This thesis aims to explore the effects caused by the presence of Grassmann numbers in two different frameworks derived from AdS/CFT correspondence: purely fermionic sigma-models and fluid/gravity correspondence. The first analysis we present deals with fermionic sigma-models constructed by means of purely fermionic coset spaces, namely we consider models with anticommuting target-space fields only. We notice that the Grassmanian behaviour of the fields implies several simplifications when we derive the action and the radiative corrections, however it provides obstructions to some supercoordinates transformations. In the second part of the work we extend the fluid/gravity correspondence by considering supergravity theories in the bulk and computing the black hole superpartner. The resulting metric is a black hole solution of the supergravity equations of motion and its associated charges and entropy depend upon Grassmann numbers. Moreover by fluid/gravity techniques we find that also the fluid dynamics parameters, such as the temperature and the velocity, are in general affected by Grassmann numbers.