Estimation of the Lin-Yang bound of the least static energy of the Faddeev model

TL;DR

This paper investigates the upper bound of the least static energy in the Faddeev model with fixed Hopf index, providing a numerical estimate for the coefficient c that is significantly smaller than recent analytical results.

Contribution

The paper introduces a numerical approach to estimate the Lin-Yang bound coefficient c for the Faddeev model, improving upon previous analytical estimates.

Findings

Numerical estimate of the coefficient c is significantly smaller than recent analytical values.

Constructed explicit trial configurations for the Faddeev field n.

Provides insights into the energy bounds of the Faddeev model.

Abstract

Lin and Yang's upper bound E_Q <= cQ^(3/4) of the least static energy E_Q of the Faddeev model in a sector with a fixed Hopf index Q is investigated. By constructing an explicit trial configuration for the Faddeev field n, a possible value of the coefficient c is obtained numerically, which is much smaller than the value obtained quite recently by analytic discussions.