Protected couplings and BPS dyons in half-maximal supersymmetric string vacua.

We analyze four- and six-derivative couplings in the low energy effective action of D = 3 string vacua with half-maximal supersymmetry. In analogy with an earlier proposal for the ( ∇ Φ ) 4 coupling, we propose that the ∇ 2 ( ∇ Φ ) 4 coupling is given exactly by a manifestly U-duality invariant genus-two modular integral. In the limit where a circle in the internal torus decompactifies, the ∇ 2 ( ∇ Φ ) 4 coupling reduces to the ∇ 2 F 4 and R 2 F 2 couplings in D = 4 , along with an infinite series of corrections of order e − R , from four-dimensional 1/4-BPS dyons whose worldline winds around the circle. Each of these contributions is weighted by a Fourier coefficient of a meromorphic Siegel modular form, explaining and extending standard results for the BPS index of 1/4-BPS dyons. [ABSTRACT FROM AUTHOR]