SYMMETRY RESTORATION IN THE SUPERSTRING THEORY

Abstract

The grand unified gauge group G 6≡ SU (3) C × SU (3) L × SU (3) R , which results from compactification of the heterotic superstring onto a three-generation Calabi–Yau space as a maximal subgroup of E 6, contains two superfields, whose scalar components are the conjugates neutrino [Formula: see text] and the neutral Higgs N, which are singlets of the standard-model gauge group G 4≡ SU (3) C × SU (2) L × U (1) Y , and which therefore break G 6to G 4 when they acquire non-vanishing vacuum expectative values. Here, we show how this process can be implemented in two steps when the scalar potential V(ϕi) is chosen along a non-D-flat direction, using the "superconducting" model due to Mohapatra and Senjanović, in which one of two scalar fields remains in the asymmetric state up to a temperature T0~ 1017 GeV , above which the kinetic energy exceeds the potential drop, forcing restoration of the symmetry below the compactification scale T c ≈ 1017 GeV . This implies that [Formula: see text] initially, but at low temperatures T ≪ M w , we find that [Formula: see text], thus avoiding the problems associated with large intermediate scales M I ≳ 109 GeV while keeping the Higgs mixing term ~ NH1H2 at the right level. A discrete gauge symmetry can prevent the proton from decaying too rapidly.