  In this paper, we provide a general classification of supersymmeric
QFT$_{4}$s into three basic sets: ordinary, affine and indefinite classes. The
last class, which has not been enough explored in literature, is shown to share
most of properties of ordinary and affine super QFT$_{4}$s. This includes,
amongst others, its embedding in type II string on local Calabi-Yau threefolds.
We give realizations of these supersymmetric QFT$_{4}$s as D-brane world volume
gauge theories. A special interest is devoted to hyperbolic subset for its
peculiar features and for the role it plays in type IIB background with non
zero axion. We also study RG flows and duality cascades in case of hyperbolic
quiver theories. Comments regarding the full indefinite sector are made.
