Uniform-limit renormalization for ultralocal lattice regularizations of sigma models

Determine whether the vacuum density of ultralocal lattice regularizations of non-ultralocal sigma models, particularly the principal chiral field, has a uniform continuum limit through a factor multiplying the box length, and characterize the form of that factor.

Background

The paper proposes that, for the sine-Gordon model, the dependence on the lattice cutoff can be absorbed into a multiplicative factor Z_L multiplying the box length. This produces a uniform continuum and infinite-volume limit while leaving the continuum mass and coupling parameters non-running. The authors suggest that the construction may extend to other ultralocal integrable theories with massive spectra.

Asymptotically free sigma models, including the principal chiral field, present a technical obstacle because their classical Poisson structures are non-ultralocal. Although ultralocal lattice regularizations have been constructed for such theories, the paper does not establish whether their vacuum densities admit the same type of uniform limit or determine the corresponding cutoff-dependent length factor. Resolving these questions would test whether the proposed renormalization interpretation extends beyond sine-Gordon theory.