Helicity modulus as renormalized coupling in the O(3) sigma-model

TL;DR

This paper introduces the helicity modulus as a nonperturbative, finite-volume renormalized coupling in the O(3) sigma-model, establishing its universal relation to the massgap coupling through analytical and numerical methods.

Contribution

It defines and analyzes the helicity modulus as a new finite-volume coupling in O(n) models, connecting it to the massgap coupling universally across scales.

Findings

Helicity modulus serves as a finite-volume coupling similar to the Schrödinger functional.

Universal relation established between helicity modulus and massgap coupling.

Analytical and numerical methods confirm the continuum limit connection.

Abstract

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.