Dynamical symmetry breaking in hyperbolic 4D spacetime and in extra dimensions

We study the dynamical symmetry breaking in quark matter within two different models. First, we consider the effect of gravitational catalysis of chiral and color symmetries breaking in strong gravitational field of ultrastatic hyperbolic spacetime a"e aSu H (3) in the framework of an extended Nambu-Jona-Lasinio model. Second, we discuss the dynamical fermion mass generation in the flat 4-dimensional brane situated in the 5D spacetime with one extra dimension compactified on a circle. In the model, bulk fermions interact with fermions on the brane in the presence of a constant abelian gauge field A (5) in the bulk. The influence of the A (5)-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable.