Determination of the superstring moduli from the higher-derivative terms

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 A r ≡e 2 κ 0σ A and the radius squared of the internal space B r ≡e 2 κ 0σ A in units of the Regge slope parameter α′, and are massless at the tree level, where A r≈ g −2 defines the gauge coupling, and when higher-order gravitational effects are ignored. Here, we show that the higher-derivative terms R ̂ 2 and R ̂ 4 in the ten-action Ŝ give rise, via the corresponding dimensionally reduced terms R and R 2 in S, to contributions A r R E 2,B r −3R and B r −2 R 2 to the potentials V( σ A ) and V( σ B ). These became large at the compactification era, suggesting why the gauge coupling is strong initially, A r∼1, and why the compactification scale is of order unity, B r∼1.