Stringy sphalerons and Gauss-Bonnet term

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 β 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 β below certain critical values βN 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 β above critical values, in particular, for β = 1.