Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form F (Φ) (∇Φ) 4 in a class of string vacua known as CHL Z N heterotic orbifolds with N prime, generalizing our previous work which dealt with the case of heterotic string on T 6 . We derive the Ward identities that F (Φ) must satisfy, and check that our formula obeys them. We analyze the weak coupling expansion of F (Φ), and show that it reproduces the correct treelevel and one-loop contributions, plus an infinite series of non-perturbative contributions. Similarly, the large radius expansion reproduces the exact F 4 coupling in four dimensions, including both supersymmetric invariants, plus infinite series of instanton corrections from half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS dyons in 4 dimensions in all charge sectors. In the process we clarify several subtleties about CHL models in D = 4 and D = 3, in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits.
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