  We consider the possible existence of gravitationally bound stringlike
objects in the framework of the generalized hybrid metric-Palatini gravity
theory, in which the gravitational action is represented by an arbitrary
function of the Ricci and of the Palatini scalars, respectively. The theory
admits an equivalent scalar-tensor representation in terms of two independent
scalar fields. Assuming cylindrical symmetry, and the boost invariance of the
metric, we obtain the gravitational field equations that describe cosmic
stringlike structures in the theory. The physical and geometrical properties of
the cosmic strings are determined by the two scalar fields, as well by an
effective field potential, functionally dependent on both scalar fields. The
field equations can be exactly solved for a vanishing, and a constant
potential, respectively, with the corresponding string tension taking both
negative and positive values. Furthermore, for more general classes of
potentials, having an additive and a multiplicative algebraic structure in the
two scalar fields, the gravitational field equations are solved numerically.
For each potential we investigate the effects of the variations of the
potential parameters and of the boundary conditions on the structure of the
cosmic string. In this way, we obtain a large class of stable stringlike
astrophysical configurations, whose basic parameters (string tension and
radius) depend essentially on the effective field potential, and on the
boundary conditions.
