Abstract :
The dimensionally reduced, heterotic superstring four-action S contains two scalar fields which are the real parts of two complex chiral superfields, termed the moduli. They describe the dilaton Ar≡e2κ0σA and the radius squared of the internal space Br≡e2κ0σA in units of the Regge slope parameter α′, and are massless at the tree level, where Ar≈g−2 defines the gauge coupling, and when higher-order gravitational effects are ignored. Here, we show that the higher-derivative terms R̂2 and R̂4 in the ten-action Ŝ give rise, via the corresponding dimensionally reduced terms R and R2 in S, to contributions ArRE2,Br−3R and Br−2R2 to the potentials V(σA) and V(σB). These became large at the compactification era, suggesting why the gauge coupling is strong initially, Ar∼1, and why the compactification scale is of order unity, Br∼1.
