  For the family of O(n) invariant nonlinear sigma-models we consider boundary
conditions that are periodic up to an O(n) rotation. The helicity modulus is
related to the change in free energy under variations of the corresponding
angle. It defines a nonperturbative finite volume running coupling similar to
the Schr"odinger functional for QCD. For the two-dimensional O(3)-model we
investigate this quantity by analytical and numerical techniques. We establish
its universal continuum relation to the finite volume massgap coupling at all
scales and coupling strengths.
