Helicity modulus as renormalized coupling in the O(3) σ-model Original Research Article

For the family of O(n) invariant nonlinear σ-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 Schrödinger 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.