Self duality of the gauge field equations and the cosmological constant

This paper considers the Einstein equations coupled with the nonabelian gauge and Higgs fields. It is shown that, when cosmic string solutions are sought in the Einstein-Georgi-Glashow system and the Einstein-Weinberg-Salam system governing the gravitational-electromagnetic-weak interaction forces, the self duality conditions lead to positive values of the cosmological constant which can be expressed by some fundamental parameters in particle physics.