STRINGY SPHALERONS AND GAUSS--BONNET TERM

TL;DR

This paper investigates how the Gauss--Bonnet term influences the existence and properties of regular stringy sphaleron solutions in SU(2) gauge theory, revealing critical parameter thresholds for their existence.

Contribution

It demonstrates the dependence of regular solutions on the Gauss--Bonnet coupling and establishes the relation between ADM mass and dilaton charge for these solutions.

Findings

Regular solutions exist below certain critical values of the Gauss--Bonnet coupling.

The ADM mass equals the dilaton charge for all static spherically symmetric solutions.

No solutions are found for coupling values above the critical thresholds.

Abstract

The effect of the Gauss--Bonnet term on the SU(2) non--Abelian regular stringy sphaleron solutions is studied within the non--perturbative treatment. It is found that the existence of regular solutions depends crucially on the value of the numerical factor $\beta$ in front of the Gauss--Bonnet term in the four--dimensional effective action. Numerical solutions are constructed in the N=1, 2, 3 cases for different $\beta$ below certain critical values $\beta_N$ which decrease with growing N (N being the number of nodes of the Yang--Mills function). It is proved that for any static spherically symmetric asymptotically flat regular solution the ADM mass is exactly equal to the dilaton charge. No solutions were found for $\beta$ above critical values, in particular, for $\beta=1$.