Abstract
In higher-dimensional supersymmetric theories gauge couplings of the effective four-dimensional theory are determined by expectation values of scalar fields. We find that at temperatures above a critical temperature T∗, which depends on the supersymmetry breaking mass scales, gauge couplings decrease like T−α, α>1. This has important cosmological consequences. In particular it leads to a relic gravitino density which becomes independent of the reheating temperature for TR>T∗. For small gravitino masses, m3/2⪡mg̃, the mass density of stable gravitinos is essentially determined by the gluino mass. The observed value of cold dark matter, ΩCDMh2∼0.1, is obtained for gluino masses mg̃=O(1 TeV).
Highlights
In higher-dimensional supersymmetric theories [1], where the standard model emerges as low-energy effective theory, gauge and Yukawa couplings are determined by expectation values of gauge singlet ‘moduli’ fields
In the following we study the dependence of gauge couplings on temperature
‘Vacuum alignment’ at high temperatures causes a power-like decrease of gauge couplings
Summary
In higher-dimensional supersymmetric theories [1], where the standard model emerges as low-energy effective theory, gauge and Yukawa couplings are determined by expectation values of gauge singlet ‘moduli’ fields. One obtains for the 4d gauge coupling and for the gaugino mass, V gD2 At finite temperature the gauge kinetic term acquires an expectation value which leads to a force on the scalar field φ.
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