Fine Tuning in Lattice SU(2) Gluodynamics vs Continuum-Theory Constraints

TL;DR

This paper investigates the coexistence of ultraviolet divergent monopoles and vortices with physical scaling in lattice SU(2) gluodynamics, examining continuum constraints to understand the fine tuning of non-perturbative fluctuations.

Contribution

It analyzes how continuum theory constraints are satisfied by lattice data, revealing the monopoles' localization on a two-dimensional subspace.

Findings

Monopoles are confined to a 2D subspace within 4D space.

Ultraviolet divergences are compatible with physical scaling.

Continuum constraints are satisfied in a non-trivial manner.

Abstract

Recently, it has been observed that the non-Abelian action associated with lattice monopoles and vortices is ultraviolet divergent, at least at presently available lattices. On the other hand, the total length of the monopole trajectories and area of the vortices scale in physical units. Coexistence of the two different scales, infrared and ultraviolet, for the same vacuum fluctuations represents a fine tuning. To check consistency of the newly emerging picture of non--perturbative fluctuations we consider constraints from the continuum theory on the ultraviolet behaviour of the monopoles and vortices. The constraints turn to be satisfied by the data in a highly non-trivial way. Namely, it is crucial that the monopoles populate not the whole of the four dimensional space but a two-dimensional subspace of it.