  We study a class of one-dimensional models consisting of a frustrated
(N+1)-leg spin ladder, its asymmetric doped version as a special example of a
Luttinger liquid in an active environment, and the N-channel Kondo-Heisenberg
model away from half-filling. It is shown that these models exhibit a critical
phase with generally a non-integer central charge and belong to the class of
chirally stabilized spin liquids recently introduced by Andrei, Douglas, and
Jerez [Phys. Rev. B 58, 7619 (1998)]. By allowing anisotropic interactions in
spin space, an exact solution in the N=2 case is found at a Toulouse point
which captures all universal properties of the models. At the critical point,
the massless degrees of freedom are described in terms of an effective S=1/2
Heisenberg spin chain and two critical Ising models. The Toulouse limit
solution enables us to discuss the spectral properties, the computation of the
spin-spin correlation functions as well as the estimation of the NMR relaxation
rate of the frustrated three-leg ladder. Finally, it is shown that the critical
point becomes unstable upon switching on some weak backscattering perturbations
in the frustrated three-leg ladder.
