On the Continuum Limit of Topological Charge Density Distribution

TL;DR

This paper investigates the continuum limit of topological charge density distribution using lattice data and sigma-model embedding, revealing a three-dimensional structure and linear divergence in the topological density.

Contribution

It proposes a novel scenario linking the UV divergence of topological density to the dimensionality of sign-coherent regions, supported by lattice data analysis.

Findings

Topological charge regions are likely three-dimensional.

The topological density exhibits linear divergence in the continuum limit.

A parameter-free method to analyze topological fluctuations is introduced.

Abstract

The bulk distribution of the topological charge density, constructed via HP^1 sigma-model embedding method, is investigated. We argue that the specific pattern of leading power corrections to gluon condensate hints on a particular UV divergent structure of HP^1 sigma-model fields, which in turn implies the linear divergence of the corresponding topological density in the continuum limit. We show that under testable assumptions the topological charge is to be distributed within three-dimensional sign-coherent domains and conversely, the dimensionality of sign-coherent regions dictates the leading divergence of the topological density. Confronting the proposed scenario with lattice data we present evidence for indeed peculiar divergence of the embedded fields. Then the UV behavior of the topological density is studied directly and is found to agree with our proposition. Finally, we introduce parameter-free method to investigate the dimensionality of relevant topological fluctuations and show that indeed topological charge sign-coherent regions are likely to be three-dimensional.