Exact topological density in the lattice Skyrme model

TL;DR

This paper introduces a lattice Skyrme model with a novel local topological density based on tetrahedral volumes in S^3, enabling effective meson-baryon interaction modeling and revealing unexpected results in skyrmion size calculations.

Contribution

It presents a new method to define topological density on a lattice using Coxeter's Schlafli function, advancing the modeling of meson-baryon interactions.

Findings

Calculated the mean-square radius of a skyrmion.

Discovered surprising results in skyrmion size.

Proposed a lattice formulation for the Skyrme model.

Abstract

We propose using the Skyrme model on a lattice as an effective field theory of meson-baryon interactions. To this end we construct a local topological density that involves the volumes of tetrahedra in the target space S^3 and we make use of Coxeter's formula for the Schlafli function to implement it. We calculate the mean-square radius of a skyrmion in the three-dimensional Skyrme model, and find some surprises.